Yes, you can search the 1940 census for residence in 1935. Searching only for those who were in different places in 1935 and 1940 is not directly possible (unless you know the 1940 location), although scanning the search results will identify any 1940 residences that don't match the 1935 value.
At ancestry.com
- go to 1940 United States Federal Census
- use the "Any Event" field, specify 1935 (exact) and the location
ancestry has indexed "Inferred Residence in 1935" & "Residence in 1935"
At familysearch.org
- go to United States Census, 1940
- use the "Residence in 1935" life event field, specify 1935 (exact) and the location
familysearch calls the field "Last Place of Residence" (without specifying the year) on the individual's record page
You can also try searching from the general search pages, using the "residence" field at ancestry.com or the "any" life event field at familysearch.org, then filtering to drill down to the 1940 census. In addition to more steps, you are likely to have a lot of extra results, including those born in 1935 in that location (especially at familysearch).
In all cases, the results will include a lot of people who didn't move outside the city or county between 1935 and 1940.
Notes:
- Non-urban areas are designated "Rural," or omitted, in the city field of the census page), so many placenames won't be specified in the 1935 residence field.
- Informants are identified in the census. The person(s) you are looking for may not have supplied the information for their household.
- Depending on the location, city and county directories may be a more direct way of searching.