Does an insurance company have the right to hire private investigators to take an EUO statement?

I think you are saying that an EUO (examination under oath) is being required by the insruance company because your car was stolen.  However, your car has now since been recovered.  I take it from your question, they are still wanting to investigate you by requesting tax returns and w2’s. There is a clause in your insurance policy that give the right to an insurance company to investigate a claim and it also bounds you to cooperate.  However, I would be leary of any ecamination under oath.  Contact an attorney in your area and ask if there should be an attorney present when you submit to an EUO? Also ask about the other documentation they are requesting. You can find an attorney in your area by clicking here