For general titles on particular states and their political environment and context, try a search in DiscoverE such as:
Woodruff Library has actively been collecting and adding text books and scholarly studies of state politics. Textbooks are often a popular place to acquire basic information on the legislative and executive policy making process and context of each state over time. We recently acquired many new state-specific titles, and more are on order (including new editions of existing texts). Be sure to use bibliographies as necessary in these titles to further your research and build your references. You may also need to use interlibrary loan for some titles. Check for availability of titles via worldcat.
Statistical abstracts are also good places to commence your research on individual states.
For comparative statistics, you may also wish to check out the Statistical Abstract of the U.S. and/or the City and County Databook. Older editions of the Statistical Abstract are available in print, or online via the Census.
NOTE as well that in many cases there will be edited volumes that have chapters dedicated to specific states or geographical regions of the U.S. In many cases, the library's catalog includes and incorporates tables of contents for said volumes. With that said, just type in your state and politics in the searchbox.
Finally for good comparative studies, you may wish to consider the Book of the States, available since the 1940s.