Tenant asking to install a nest/ring doorbell

So here’s the situation, we currently live in a duplex that we own. The doors for each unit are outside and side by side. We currently have a nest that faces the stairs that lead up to the doors so we can see who comes and goes to either unit.

We just signed a new lease with a tenant and they asked about installing their own nest or ring doorbell. My issue is privacy, I don’t want a tenant to see who comes and goes from my house or any convo’s I’m having with anyone.

I would think their security isn’t a valid reason since we already have one so that box is checked. I wouldn’t have an issue with sharing a video clip if something were to happen. It would really only be for their convenience of not having to come downstairs if they didn’t have to. 

Would you be okay with it as a landlord ?

Is it legal to tell them no ? This is in NYC.