The main database for researching state administrative law is Lexis Academic. After opening Lexis, choose "US Legal" from the side menu and then choose "State Statutes, Codes & Regulations".
On that page, you can choose the state you would like to search in by using the "jurisdiction" drop down menu, and then choose the state's administrative code in order to search for state regulations.
Lexis Academic also provides state register publications, which publish rule and regulation updates. These can be accessed by doing a "Find Sources" search under the "Sources" tab on the side menu.
Another important source for state administrative law is the websites of the state agencies and legislative bodies. Often times the websites will have links to administrative codes and regulatory material, contact information, and other helpful resources for legal research. Secretary of State websites often house regulatory and administrative materials.