Would a US immigrant from Germany traveling back to Germany in the 1850's have a passport.
Where are these records?
For an overview of the holdings available at the National Archives and Records Administration (NARA), see: Research Our Records: Passport Applications. (Their research guide was adapted from: Kathie O. Nicastro and Claire Prechtel-Kluskens, "Passport Applications: A Key to Discovering Your Immigrant Ancestor's Roots," Prologue: Quarterly of the National Archives 25 (Winter 1993): 390-394. This article is not online -- search WorldCat for a library near you.)
The Department of State has been issuing passports since 1789; NARA has passport applications as old as 1795. However, passports haven't been required until 1941, except in wartime.
Aliens (people who were not yet naturalized) were not eligible to get a passport, but NARA says there are two exceptions:
NARA advises to search for passports during the person's entire lifetime, because people often traveled multiple times. You may not be able to find the passport for the trip in the 1850s that you know about, but you might be able to find one for a later trip.
A list of records from the Department of State that been digitized and are available at all NARA facilities can be found on NARA's page Genealogical Records.
Diane L. Richards' US Passport Records Online is a brief article introducing Ancestry's collections (downloadable PDF).
For passports issued in the USA, Ancestry.com's Card Catalog has:
Note that NARA's holdings will only cover passports issued by the Federal Government. If Ancestry has holdings for passports issued by the state of Connecticut, then other state-issued passports might exist -- try searching the State Archives or State Library or other local archives for the places your immigrant lived in. Also check local public libraries for guides to genealogical records in that area. See How can I determine what records are available in a particular locale? for ideas of how and where to search.
General information about Federal passports:
For general guides on how to navigate the holdings at the National Archives, see:
Normally U.S. citizens did not need passports except during times of war. But they did need identification papers which could be as simple as a letter by a local official or family priest. Naturalized citizens would be more likely to get a passport. I've found some post-1890 examples on Ancestry.com
Passports became mandatory during WWII -- https://en.wikipedia.org/wiki/United_States_passport#History