There are 2 listed for Ohio. Hopefully one of those folks will be able to give you some solid answers.
Many times, a health certificate from a veterinarian is a an acceptable document. And Most states have slightly different rules so I would think for your NPIP to stand after moving you would need to do it at your new location again... if you still needed it for shipping eggs, chicks, or birds and not just for your move. Sorry for raising more questions.