Can I charge an inherited tenant for cleaning when they leave?

[Belinda Stoner]

I recently closed on a two-family in New Orleans. My daughter, who attends school there, will live in one side, and I plan to use the other side as a STR. The tenant who currently lives in the side my daughter will live in was given a notice to vacate, and she'll be out by the end of next month. She was a long-term tenant (nine years) and, judging from what I saw when I went through the place, didn't do a lot of deep cleaning while she was there. I mean the place wasn't trashed, but it was definitely pretty dingy.

This is my first time buying a place with existing tenants. With other tenants, I provide a list at move-in of the tasks they will be expected to complete at move-out if they want to receive their deposit back. I even include the amount I will charge for each task that isn't completed--for instance, not cleaning out the oven incurs an automatic $150 charge. 

Since I have no way of knowing what shape the place was in when she moved in nine years ago, can I still do this? It seems like I should be able to. But who knows? With all of the crazy laws out there "protecting" tenants from us greedy landlords, I thought I'd check.

Thanks for any input you can offer!