Is it legal to contract with an online background search site to gather information about an individual who stole my identity?

I am a lawyer in CT and practice in this area of the law.  Identity theft is unlawful in every state.  If you believe that someone stole your ID, then you need to report it to the police, notify the 3 major credit reporting agencies and all your credit cards.  If you do not think that the police are helping, then you may contract with a company as you describe here to conduct you own independant invenstigation.  If you find out who the person it, you need to report it immediately- DO NOT TRY TO TAKE THE LAW INTO YOUR OWN HANDS.