Dear Mr. Cooper,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Muster Rolls of Naval Ships and Shore Establishments, 1/1898 - 6/30/1939 that may include muster rolls for the USS Connecticut (BB-18) as well as Navy shore establishments in the Great Lakes area. We also located the Logbooks of U.S. Navy Ships, 1801 - 1940 in the Records of the Bureau of Naval Personnel (Record Group 24) that include the deck log of the USS Connecticut for 29 September 1906 through 1 March 1923. While deck logs rarely include names of individual enlisted personnel, they provide information about the activities of a ship. There also may have some pay records for this time period, but there are gaps in the collections. For access to these records, please contact the National Archives in Washington DC - Textual Reference (RDT1) via email at firstname.lastname@example.org
We hope this information is helpful. Best of luck with your research!
Thank you Jason this gives me a better starting point.