Should I file police report if someone threatened my pets?

Without reading the lease there is no way to know.

What would I do based on my legal training and experience?

I'd remove my cats from the premises, and that might involve boarding them.

I'd then notify the Police of the threat. Will they investigate? Almost definitely not. Will there be a Police report? Yes.

Will your landlord allow you to break your lease based on threats? I don't know. I would have to read the lease, and I would have to speak with your landlord.

Yeah right; and then the cowardly police show up to kill your cats.

Don't call the police. Clean your own dirty laundry.

it would be far more effective if you kill the cats then report her.

Absolutly file a police report. Having the threats on video may be enough so your landlord can allow you to break lease. Although it's not a good idea, I had a tenant once who got a restraining order against a boyfriend so I had to let them out of the lease.

many states have changed the law to allow a lease to be broken in cases of domestic abuse . ask the police about it while you are filling out the paperwork .

If you have it on video report it to the police. It won't help you break your lease. Ask your landlord as he may agree to it.