Returning Deposit: Sending Certified Mail vs. Bank Deposit

[Dana Holland]

My tenants are moving out and I sent them a letter informing them of the process for the move out inspection as well as returning their deposit.  I asked for a forwarding address to send the deposit via certified mail.  They don't want to give their new address for whatever reason and are asking me to deposit funds in their bank account instead.  I wanted to do certified mail so that I have proof that it was received.  Will the bank deposit be as safe of a method?