You should seek legal assistance about process service. The answer varies by state law and by court.
In general, a litigant could consider whether the bank maintains an agent for service of process within a particular state, although national banks and federal savings associations may not necessarily have registered agents in each state. A litigant also could consult the relevant court's rules for serving process on an out-of-state corporation that does not maintain an agent for service of process.
If you need the bank's address, you may want to go to the FDIC's website (www.fdic.gov). Select BankFind in the right-hand corner.