You have two issues here. First is BSA, which requires 5 year retention. My source cites 31 CFR 103.34(b)(1) and 31 CFR 103.38(d).
The other is your state's statute of limitations. In Michigan, since the signature card grants signature authority, it may be relevant in breach of contract situations - it's recommended we keep them for 6 years after the account is closed. Your state may have different requirements.
The answers above both apply whether it's a checking or a savings account.
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