No. Closing your old checking or savings account won't hurt your credit score the way closing a credit card or line of credit would. The only way it can indirectly impact your credit score is if the bank forced the account closure because of outstanding fees that you did not pay in a timely manner and that were sent to a collection agency.
As long as it was a regular checking or savings account (basically any non-credit card account or other loan account), it shouldn't. Checking and savings accounts are not reported to the credit bureaus and are not factored into your credit score. If it is an old credit card, it could impact your credit score as it would lower your total credit line available (and potentially increase your credit utilization ratio) and it might decrease the average length of your credit history. Both of those can have a negative impact on your credit score.
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