The Department of Consumer and Industry Services provides an online look-up of state-chartered banks and a list of state-chartered savings banks. 

Chartered Bank Lookup - Banks are for profit shareholder owned financial institutions that are authorized to accept deposits, make loans, and engage in a variety of other financial transactions. For purposes of this listing the banks are all state-chartered and currently operating. Savings banks, national banks, federal savings banks, and federal savings and loan associations are not listed.

Chartered Savings Bank Listing - Savings banks are for profit financial institutions that are authorized to accept deposits, make loans, and engage in a variety of other financial transactions. However, savings banks may either be mutual in form or owned by shareholders. By statute, savings banks are required to meet an asset test that requires a specified level of their assets be in mortgage related loans and investments. For purposes of this listing, the savings banks are all state-chartered and currently operating. State banks, national banks, federal savings banks, and federal savings and loan associations are not listed.