Lexis-Nexis Academic is the best database the library has for finding state cases or information about state cases. On the front page of the database you can:
Depending on what you are interested in, next choose either Federal & State Cases or State Statutes, Codes & Regulations.
Search by keyword and limit to the jurisdiction you are interested in. You have several choices here; you can limit to a particular state or to all state high courts.
You can limit even further on the results screen by using the facets on the left side of the page to choose the date range and the court in which you are most interested.