This is governed by the Patriot Act and it matters not whether the bank is State or federally regulated bank. All banks are required to adopt a Customer Identification Program [CIP]. The CIP Rule requires banks to adopt written procedures to ensure proper identification of customers.
The Rule allows great flexibility for each institution to adopt procedures appropriate to its own size and customer base. This means the procedures may vary significantly from one company to the next. One bank, for example, may require you to submit only one item of identity while another may ask for several pieces of identification. The bank also has discretion to decide which form of ID it is willing to accept. So, the answer to your question is "Yes"; but you may want to ask for a copy the bank's written policy regarding acceptable forms of ID and see what other options you have; such as a passport or birth certificate.
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