Create a biographical sketch and timeline, and a research plan. To find his records in any archive, first you need to have enough specific information to be sure that you are asking about the right individual.
You read newspaper accounts in the scrapbook, so if you don't have access to the scrapbook, step one would be to find the newspaper accounts, and his obituary. Newspaper sites like Genealogy Bank, Newspaper Archive, Google News Search, etc. might be available for search at your local public library if you can't afford a subscription. When looking for an obituary, put in 1968, but search for a range around that year in case your father's memory of the date of death is not quite accurate. Use a keyword search to look for combinations of the keywords in your original question. (SS = special services)
Assemble the information you find in chronological order to make a timeline.
The purpose of this is to make it easier to ask for and find any records which might exist. The problem with genealogy these days is that advertising from big sites like Ancestry.com encourage us to start immediately searching by name when there are other things we need to consider first. Find his date of death and work backwards from there. Use what you find as the basis for other research questions. Which radio station was it? How long did he work there? When was his retirement from the BPD? How long was his career?
There's a huge difference between asking someone "Do you have any material on Francis Murphy?" and "Where can I find records about members of the Boston Police Department who served in the period 1940-1970? The detective I'm researching worked in special services and retired in 1965."
As you've seen, if you ask the question the first way, especially with a common name like Murphy, you'll get the answer that there are too many Murphys to answer your question; if you ask the second way, you may get the answer that BPD service records are not available to the public, or they might be able to direct you to someone who might know (e.g. at the City Archives). After you find a collection of records that might be relevant, then you ask "is there anyone named Francis Murphy in this collection?" and "How can I tell if this Francis Murphy is the one I'm looking for, or someone else with the same name?"
After gathering more information, if I wanted to hunt down the service records, I might search at the Boston City Archives or seek help from the reference desk of the Boston Public Library. I would expect much more information to be available locally and off-line than I could find myself using online services, but before I reached out to those organizations I would collect whatever I could find that might help identify the person I wanted to research. I would also expect that some records would not be available due to privacy concerns.
If I could not research in person, after assembling a precise set of questions that I wanted to know the answers to, and establishing a budget, I would consider hiring a professional genealogist. But no matter who does the search -- whether you do it yourself, or whether you hire someone to do it for you -- the search will be far more productive if you have a clear picture of what you want to know, and search for the answers to specific, focused questions.
Pay close attention to the specific information you find in any records or newspaper accounts you seek; when you search for more records, it helps to record and use the specific language that the records themselves will use. Researching the general background of the city and the Police Department gives context for what you find -- if you find important events, add that background information to your timeline as well.
For example: according to the newspaper the Boston Record American, in February of 1964 the special service squad was broken up and the men were transferred to other units (Source: Genealogy Bank; published on Thursday, February 27, 1964, in the Boston Record American (Boston, MA). page 4, column 1). This fact now gives you two things to search for -- before 1964, you search for references to the special service squad; after the reorganization, you search for the Criminal Investigative Division (CID).
In this particular case, it is especially helpful to study Murphy's associates. Collect the names of other detectives and officers who are mentioned in the newspaper articles that you find him in. Searching for their names may help you find other newspaper articles in which Murphy also appears. Newspapers are often transcribed or indexed by computers using a process called optical character recognition (OCR), which isn't perfect. You can't depend on every instance of 'Murphy' being transcribed as 'Murphy' because the computer can make a mistake. (One common mistake seen in Ancestry's City Directories: the middle initial H is read as II.)
Displays of search results and articles displayed from the search may also be limited on how many hits they report per page. If you search for 'funeral' on Genealogy Bank and choose the setting that highlights the word 'funeral' on the chosen newspaper page, it may only highlight the first several instances of the word, so if you have an entire page of funeral notices, look at the entire page to make sure the notice you seek isn't buried at the bottom without a highlight.
A brief death notice for retired police detective Francis J. Murphy was published in the newspaper Boston Record American (Boston, Massachusetts) in the Saturday, December 16, 1967 issue, page 21, column 1, and can be seen at Genealogy Bank (requires a subscription). According to the article, he worked for the department for 20 years (many of them on special services) and for radio station WHDH for two years as their head of security.
Another brief article appeared in the Boston Herald (Boston, MA) the following day (Sunday, December 17, 1967, page 64, column 3). The Herald says that he was appointed to the Boston police department Dec 18, 1946, and was assigned to District 19, Mattapan, before he got the assignment to the Special Service squad at headquarters. "He subsequently was promoted to first grade detective and assigned to the headquarters detective bureau for city-wide investigative assignments."
Working backwards from this date, and varying the keywords, you can find other articles.
If you don't want to subscribe to Genealogy Bank, you may be able to access these articles at your local public library, if your library has NewsBank (both are owned by ProQuest). WorldCat lists some holdings for the Boston Record American at the Library of Congress and at the State Library of Massachusetts (in Boston). Wikipedia's list of online newspaper archives may also be useful.
When using any library or online subscription service, make a note of the coverage for the collection you have searched -- collections are often incomplete, and one repository may have issues of a newspaper that another one lacks.
His police service records may not be accessible to the public; if you want to hire a professional, be prepared to provide proof of your relationship.
Another thing to consider: Boston historical societies and/or genealogical societies might be able to help you. For instance, the New England Historical and Genealogical Society (NEHGS), which is based in Boston, has both free events which are open to the public, and paid workshops for people who want to learn more about their family history. (One such example: "The New England Historic Genealogical Society is participating in the Free Fun Fridays program sponsored by the Highland Street Foundation. On Friday, July 11, 2014, NEHGS will open our doors at no cost to visitors all day long." NEHGS also has free 15-minute consultations, but space is limited, and you have to sign up in advance.)
If you have a digital camera or scanner, you could take photos of the scrapbook. That way the original scrapbook could stay safe at home, but you would have copies that you could take with you while you are doing research. (NEVER take originals out on the road with you -- they might be damaged or lost.)
One other thing to consider: your relative died in 1967. Reading the scrapbook of his cases, which were written as they happened, will leave you with a feeling that not much time has passed. But if you are talking about someone who served in the 1960s, fifty years have passed since then. How long is the service career of detectives like your relative? Speaking of career terms rather than lifetimes, two generations may have gone by. I would ask at the City Archives or a historical society to find out if anyone specializes in the history of the BPD -- that would be one way to find out others who may know more about your relative, or other detectives in his unit.