You could not open the landlord /tenant account in any other state then NY ....
Example the same is true for me in NJ ... I open all my tenant security accounts at Bank of America at the branch that my rentals are in.
Yes there are Bank of America's in many other states but the account has to be opened in a bank in NJ to met the requirements by NJ renting law.
So the same is true for you in NY ....
Once opened I send a certified letter to tenant which includes the following info
account #
Bank
Bank address
date of deposit
amount deposited
( this info is included in my lease as well all is filled out at lease signing [less account # which I don't know at the time ] in the same letter I include a revised lease copy to included the account number )
All the above is required by NJ law - as well as advising the tenant yearly what their interest - is usually no even a dollar - I do not allow the tenant to draw on the interest to use toward rent ( as NJ law implies ) ..... I have specific wording in my lease that says the interest will ecru till end of tenancy.
--68.197.xx.xx