Share your insights or perspective on the financial matter presented in the input.

My university has tranfered me money by mistake, and wants me to transfer it back
You have received some good answers, but since your concern is proper protocol, keep everything in writing (emails, not phone calls).  Also, you'll get a quick response by contacting the University "Accounts Payable" department, confirm the situation with a summary as you posted here and ask for the ABA routing number for the transfer.  The routing number, email, and you bank statement is all the records you need to cover your but.