We have an out of state customer who used to live here, now in State B. He has recently started a business with the parent company in yet another state, State C. He wants to open an LLC which is located in state C but the managing member who will run the LLC will be in State B. Do we need any additional information for State A where the account will be located?

First question is why someone who no longer lives in your State and does business in two other States using layered corporations needs a banking account in your State?

He is a long time good customer with ties to our area.

Then you are talking about State law as to what, if anything is required.

all things being equal, i'd bet that in 75% of all cases where banks take a loss, those very words were uttered at some point in time.

I would be asking for a copy of the Operating Agreement or state equivalent.