Can I refuse a tenant if they are not a good match with the people already living there?

[George P.]

Hello,

I have a two unit property and trying to fill a vacancy in one of the two apartments.
The one unit is currently rented by three college girls in their early twenties.
A man (45), has shown interest in the apartment. He is divorced with two kids.

I am afraid that the current tenants might feel uncomfortable with an older man in the house since there are common areas that are shared (like the laundry room in the basement). The property is an old colonial house and not an apartment building, so interactions between tenants are more frequent.

Can I refuse him the apartment based on this? Is it discrimination? Am I thinking too much about this?