Tenant Story of the Week: Ghosts? Now what?

So now what? Ghosts!

So I have a 2 family and unit 1 was vacating because they found somewhere else to live, and they did not get along with the tenants in unit 2. So the week they moved out the tenants in unit 2, 2 college men who shared a place called and said they wanted to move early because they were not getting along. I said that they needed to honor their lease. So about a week later one of them shot themselves in the apartment and committed suicide. Wait-it gets better!

So a few weeks later I rented unit 1 to a family, and unit 2 has been cleaned and rent ready and is on the market. So yesterday the new tenant in unit 1 calls and wants to know if I rented unit 2. I said no, why do you ask? She said that they think someone is living there as they have heard voices talking in the bedrooms upstairs.

Checking the unit, there is no sign of entry, no unlocked doors or windows, and no signs of anyone getting inside. What do you think I should do now? Do you believe in haunted homes? They also told me they heard a woman singing a child to sleep. It's actually freaking me out. Any ideas?