Will I be able to get my money back?

What are the police to investigate, you willingly wired a person money. The transaction was completed and you have no written contract for repayment. The bank is passing the buck to the police since THEY are not going to give your money back since you willingly did the transaction (fraud or not). The police would have advised you NOT to do the transaction BEFORE you did so and to investigate it further, but given that you willingly did the transfer, nothing they can do. They know exactly what is going on and often warn people not to fall for these scams or cash checks and wire money to people you don't know.