One night when I lived in Plano, TX I had a very similar experience. I had failed to secure my front door upon us turning in (I believe due to the stress of watching Bill Clinton re-elected that night).
About 0200 a neighbor returned home from a baby sitting gig, noticed our front door open and called 911.
First I knew of it my door bell was ringing, my old dog was barking. I grabbed my BHP au naturale and headed down the hallway towards the front door. When I saw curtains on the opposite from the front door blowing from wind I was like "uh oh".
I cautiously peeked around a corner to the front door and it was wide open and there were two Plano PD officers in my front yard, spread out a good distance and they asked me to produce some ID. I said sure and retreated to do so while setting my BHP down on a flat surface by the front door - which I announced to them and told them where to look for it.
By the time I returned with my ID they were in my home and had moved my pistol to a distant spot at the other side of the room and they checked us all out and all was good. They explained the call etc and I expressed my gratitude.
We learned later from the nervous neighbor that they had stepped in, took a quick peek then retreated to ring the doorbell.
I was very impressed by their professionalism. BTW they looked like Malloy and Reed from Adam-12.