Some state court dockets may be found in Westlaw, Lexis (Browse > Sources > By Category > Dockets), and Bloomberg Law (within the state's Laws & Regulations page). National Center for State Courts offer links to public docket search engines for state and county courts when available. Also try searching for dockets on the court's web site.
To locate state court materials not available within Westlaw, Lexis or Bloomberg Law, see Free and Fee-Based Appellate Court Briefs Online, The Sourcebook to Public Record Information : The Comprehensive Guide to County, State, & Federal Public Records Sources (2015) and A Union List of Appellate Court Records and Briefs: Federal and State (1999). Some state court materials may have to be obtained from the court's clerk office.
Some state appellate courts may make recordings of oral arguments and hearings available on their web sites.
Court rules may be found in Westlaw under Statutes & Court Rules and Lexis' Court Rules. In Bloomberg Law search for [state] court rules in the search box and select Browse TOC. Court rules may also be found within the court's web site.
Court statistics may be found on the court's web page, published in the court's administrative office annual reports.