They can go back 3 years . . . however, in case of fraud there is no time limitation. As for the state, it will depend on the state but generally states will mimic the federal government.

Since you did not mention the state you're referring to, you would have to be more specific to get an answer there, and primarily because, if the state is like Arizona, some have recently amended their tax code to go back farther. Arizona is now at 10 years.