Can a court summons be left on your door? And what can I do after this happens?

The process server must obtain permission from the court to leave the notice.
This usually happens when it is very difficult, sometimes impossible, to get someone served with the notice.
As long as the court granted permission for it to be left, then you have been served. Hell, some places will allow you to post a small add the newspaper as a form of service.
You need to appear and defend yourself, however that can be done is up to you.
If you don't show up, they will be granted a default judgment because you didn't appear.
At least go and give yourself a fighting chance.

Good Luck

Yes, the laws of service vary from state to state. Leaving it on the door is allowed in some states on some types of service. ( assuming they did confirm that was the correct house and the person did live there)
If the house was empty and no electric hooked up, obviously the perosn did not live there and that may or may not have been valid service.

Now if you find it was not valid service, guesss what, you still have to go to court and present your case that you were not property serviced, since if you just don't go, they rule against you automatically.