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Dear Mr. House,
Thank you for contacting the History Hub!
The New York State census from 1855 is available on microfilm through the New York State library system - see more on their website. As the page says, original records are kept at the county level and may not be accessible depending on their condition.
The information from the 1855 census is also available for free online from Family Search - here is their search page.
For more information on what New York State censuses are available and where they are kept, this page from GenealogyBranches.com is an excellent resource.
We wish you all the best with your research.