Information for State Governments will not be as widely available as Information for the Federal Government. Because dissemination and storage of state documents is not standardized, much of what is available will depend on how an indivdual state's government has treated the Information they've created.
As a general rule of thumb, current or very recent government information will typically be on legislator or department websites and should be very accessible; historic information on the other hand will vary greatly depending on the state, and can be very difficult to find.
Here are some resources for New York State's Government.
New York State Library
Image available at http://tomforst.com/StateCaps/NewYork/index.html
Please be aware that this is by no means an exhaustive list of State Government Documents (not even for New York). For example, Resources like www.usa.gov, books.google.com, and WorldCat can offer an array of State Documents. For additional help finding any state documents (not limited to just New York), please sign up for a Research Consultation, or feel free to contact me directly.