Dear Ms. Shaffer,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Muster Rolls of U.S. Navy Ships, Stations, and Other Naval Activities, 1/1/1939 - 1/1/1949 in the Records of the Bureau of Naval Personnel (Record Group 24) that include the muster rolls of the USS Captivate (AM-156) for 30 December 1943 through 31 May 1945. These records have been digitized and can be viewed online through the Catalog.
For the period of 1939 through 1956, muster rolls list only the names of enlisted personnel. Officers are usually listed in monthly rosters attached to the ship’s deck logs. We searched the National Archives Catalog and located the Logbooks of U.S. Navy Ships and Stations, 1941 - 1983 in Record Group 24 that include the deck logs of the USS Captivate for 30 December 1943 through 16 August 1945. For access to and/or copies of these logs, please contact the National Archives at College Park - Textual Reference (RDT2) via email at firstname.lastname@example.org.
We hope this information is helpful. Best of luck with your research!