Due to the large size of the USA, you must become a Private Investigator in the U.S. by becoming a licensed PI in the individual U.S. state you are a resident of. You can also become a PI in an American state you are not a resident of; however, if you are just starting your journey as a Private Investigator you will most likely want to become licensed in your home state.
In most of America, you can use your state PI experience and credentials to help obtain PI licenses in other American states. America has one great advantage for rookie Private Investigators: in most U.S. states you can immediately become an unlicensed PI if you work under a fully licensed American Private Investigator agency.