Why would a constable leave his card at my house?

Call him/her and see.

i had that happen to me once...i called him (which is really the only way to find out) and it turns out he was looking for our wayward niece to serve her court papers....i dont remember if i even knew where she was at the time but she had previously been living with us, which is how he knew to come to my house

Also coulda' been that something happened in your neighborhood and they wanted to know if you saw anything- a car crash, a burglary...I wouldn't freak out. If they REALLY wanted to find ya they already would have.

If you moved into your residence recently, they could be looking for someone who lived there previously. So many reasons to not worry. DezziePS has this exactly right, "If they REALLY wanted to find ya they already would have."

Had this happen when there was an uptick in breakins in our surrounding neighborhood. Just wanted to know if we had noticed anything and to put us on awares.

Also have seen them do this when they were doing a sweep to make people more aware if they are leaving their vehicles and houses unsecure. (ie, windows open and no one home, cars unlocked, valuables left out visable etc.)

I would not worry.

Call and find out! There are so many innocent reasons as to why it could be.

I wouldn't worry. I completely agree with Dezzie. They want you, they would have had you by now!
But did you call? I'm so curious now...

I'd call and find out. If he was looking for YOU in particular, he'd have just served you papers. He could be looking for information on somebody, running for re-election, who knows. It's probably not a big deal. If you're worried about it, call from a friend's number.