A Web page at the New York State Library [http://www.nysl.nysed.gov/genealogy/nyscens.htm] has county-by-county listings of the NY State censuses available there on microfilm. Records for the Tompkins County censuses are available on microfilm (must be used in person in Albany) for all the state censuses between 1825 and 1925 except 1845 and 1855. From this site: "The original records for the State's pre-1915 census are kept at the county level and are not available at the New York State Library. Contact the county clerk's office to ascertain their availability and location. Original manuscripts of the 1915 and 1925 census are maintained by the State Archives."
The Rochester (NY) Genealogical Society's (RGS) Web page on the NY state census is http://www.frontiernet.net/~halsey1/ny/ny-census.htm. This is an excellent resource, including links to colonial census data from New York. Additional information from the RGS site:
"Existing original census records are usually in the County Courthouse or with the County Historian.
The LDS Family History Library has the most complete collection of films of the New York State census. It is said that the LDS does not have every existing census. Another place that has a large collection of the New York census records is the NY State Library. To see what is in there collection, go to their New York Census page. It is important to note that none of the microfilm at the NY State Library circulates while the LDS lends all filmed census."
The RGS Web site also has a online list of the questions asked in each New York state census and a county-by-county lists of the microfilm of the schedules available for loan from the LDS Family History Centers. As of this writing, film is available from the 1825 to the 1875 census censuses.
Contact the Latter Day Saints Family History Center in Ithaca. The following information is taken from the Family History section of the national LDS Web site:
Address: 114 Burleigh Drive, Ithaca, Tompkins County, New York, United States
Hours: Wed 9am-12:30pm & 6:30pm-9pm; Thurs 9am-4pm & 6:30pm-9pm; Sun 10am-11am.
Closed: Closed the last two weeks in December.
The state census microfiche set cited above, (State Censuses: [Microfiche collection of censuses of population taken after the year 1790 by states and territories of the United States]. Millwood, NY: KTO Microfilm.(Olin Microfiche 197, Lower Level) 680 fiche), includes population counts from the New York state censuses, but it does not have detailed schedules with individual names.
A reference book on both federal and state census records for New York is
Douglas, Marilyn. New York State Census Records, 1790-1925. Compiled by Marilyn Douglas and Melinda Yates. Albany: University of the State of New York, State Education Dept., New York State Library, 1981. (Olin Reference Z 7554 .U5 D73; also ILR and Mann Reference)
See pages 37 and 56 to 59 for information on the availability of state census microfilm for New York counties.