If you do an AOA residency, you are only eligble for the AOA board certifications. I think most (if not all) AOA board certification exams have an OMM questions. I think some of the boards have an OMT Practical component as well (I think the AOBFP has it). I don't think the AOBIM have an OMT Practical component but do have OMM questions on the written exams.
One of the requirement for taking the AOA board certification exams, and ongoing requirement to maintain certification, is to be a member of the AOA in good standing. So if you do an AOA residency, or do an ACGME residency and decide to get AOA boarded for whatever reason (via Resolution 56), you will have to be a member of the AOA to remain board certified. The AOA also started doing OCC (osteopathic continuous certification) recently, similar to the MOC on the MD side.
If you do an acgme residency, or do a dual acgme/aoa residency, or do an acgme (formerly aoa post merger), you can take the ABMS members board (ABFP, ABIM, etc) ... obviously no OMM/OMT questions or practical. You do not need to maintain membership in the AOA, nor the AMA, or AAFP or ACP, etc. You do have to pay money to the relevant board (ABFP, ABIM, etc) and with the new MOC requirements, jump through more hoops to maintain certification (the AOA has the equivalent, called OCC)
/still have my Savarese book somewhere, even though last time I touched it was to refresh my OMM for COMLEX 3 many many lunar eclipses ago. Still do occasional OMT on friends/family members for MSK complaints - it's a nice tool to have in the toolbag.
