What from do I need to provide if I got an letter about adjustments from the IRS? Credit for Tax Paid to Another State - Other state return not provided.

Ok ... first the IRS is federal and has nothing to do with a state credit of anykind.   So which state is questioning the credit ?   And did you file a non resident return as well as a resident ?  Which state's did you file ?   

Did you read the state notice carefully ?   What exactly do they want ?   Just a copy of the other state return ?   If so provide the information requested as directed. 

the letter wasn't from the iRS, if it concerns taxes paid to other state

there are some possibilities.   

you were a part year resident of two or more states.   generally in this situation you get no credit for taxes paid to other states unless there is some income tax in more than one.

you worked in one state while working in another with a reciprocal tax provision.  in that case you only file in one state and since no return is required for the another state, no credit

you were a resident of one state and earned income in another.     if you used TT and prepared both state returns, TT there would be a credit.   In this situation, TT needs for you to prepare the nonresident state first and then the resident state.    if you efiled the TT would have transmitted the nonresident info to the resident state.

if you mailed it was to you to include the nonresident return with the resident return.   however,  may workers at the state tax agencies are lazy, or accident prone or untrained and throw out the nonresident return without processing it.     

follow what's stated in the letter.