Inheriting tenants at my first property

[Benjamin Lemieux]

Good afternoon,

           My offer was just accepted on my first property. It will be a 3 family home in CT. I will be owner occupying. 

      One tenant is moving out and the other the tenants lease will be ending around the time that we close. The tenant who's lease is ending is looking to move into the most expensive unit in the house ($100 more than the one they are  in now). Should I just accept that they have been  good paying tenants or do a full screening on them seeing as their lease is up and I have the opportunity? (This is a family with children) I feel like I should probably screen them but I'll take some advice from the more experienced investors on here.

Thank you,

-Benjamin Lemieux