No, a checking account is not correlated to your credit score. The only reason why you have to give your social security # is to prove that you have no outstanding debt with any other banks.
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Actually, there is a correlation. Having a checking account doesn't improve your credit score, but you can be accepted or denied an account based on it. If you have bad credit, or no credit, you may be denied from a variety of bank checking accounts.
I was told by my lawyer it does improve your credit if you keep your checking account in good standings he said the bank report it monthly to the crdit bureaus thats just what i was told