Unless you can get your parents written permission for the bank to give them your records, you won't be able to access their records without some type of subpeona or court order. Exactly what is required will depend on state laws and who regulates the bank (FDIC, OCC, OTS, FRB)
where the accounts are located. I don't know how much money is involved, but if the sum is substantial, you probably need to contact an attorney for advice. Depending on your income level, you may be eligible for some type of free or low-cost legal aid program.