The 1890 police census is available in two formats: a) digital databases, and b) microfilm. Each format is available in two locations.
Databases. Neither database provides scanned images; only indexed information abstracted from the census pages is given.
Family Search makes available scanned images of the original microfilm, but this digitized collection is only viewable from computer terminals at Family History Center locations. A digital index of the 1890 police census is available at Family Search with a free membership. However, note that the citation given in Family Search uses the term "volume" in reference to the number of the census books; also, the additional numbers in the citation are references to the microfilm collection at the Family History Library, and do not match the call numbers used by NYPL collections. It is unclear how much of the 894 census books are searchable on Family Search.
Ancestry Library Edition has indexed 26 of the 894 books, or only roughly 3 percent. Digital images of the census pages are not available. The book number and page number in the book are provided.
Microfilm. The original surviving census books were microfilmed and made available at the Municipal Archives. The microfilm at NYPL is a copy of the Municipal Archives collection.
Municipal Archives at 31 Chambers Street. Here, there are 59 rolls of 894 books.
NYPL microfilm collections located in the central library on West 42nd Street and Fifth Avenue. These reels are duplicates of the microfilm at the Municipal Library. See the catalog record for the 1890 New York City police census, which details the numbers of missing books. Note that in the catalog record, the collection is described as totaling 54 reels, with a total of 108 missing books out of the original 1,008 (this is likely because the collection at NYPL is not a 100% duplication of the collection at the Municipal Archives). The reels are all assigned the same library classmark, *ZI-562, and are then arranged in the sequence of census books in the open cabinets in Room 119. No call slip or advanced request is necessary to access these microfilms.
Although the databases are limited and incomplete, it is recommended to first exhaust these electronic resources before proceeding with the microfilm. Family Search will provide a book number which helps in determining the relevant microfilm reel, while Ancestry helps by providing a page number.