Sounds reasonable, but most police departments will not do this, even if the data is available to them and running the query is easy.
They will tell you to file a report, preferably online, which will then be incorporated in local stats, and may also be useful in your interactions with your insurance company.
But they will not do anything to help your specific case.
Oddly, this was 100% commonplace before about 2000 or so, in the US at least. Every household got a free phone book from the phone company that contained the name, address, and phone number of everyone in town. I think you could opt out, but almost no one did.
It was incredibly handy and sometimes I still miss it. I'm not 100% sure why it was considered OK for so many decades but today would be considered a PII data leak, though I suppose it being limited to your local area vs. searchable by the whole world has something to do with it.
> There have been more cases of "someone broke into my house at exactly [time]. Can you track their license plate and track them down" that I'm willing to make that tradeoff.
I'm not, especially since anecdotally, police are generally unwilling to use these tools to solve petty crime anyway.