Woke up with a fright!!!! And it was no ghost either!

woke up this morning to our house alarm going off. It was pretty much just after 5:am and it totally freaked me out. Like any annoying alarm you want to quickly turn it off as possible, but because it was the house alarm I let it go.

It must have gone off for a few minutes, my 4 year old dd was sleeping in my bed as my husband was gone for the night and we were having a sleep over.
Usually the alarm company calls when it goes off, I tried calling them with the house phone to find out what room the alarm was set off in and the phones where dead and would not come on, which freaked me out even more.

Using my cell phone, finally got ahold of alarm company, and they told me it was a bedroom window that had triggered the alarm and had I checked. I informed it them it was just me and dd and I was not going to check, and could they please send someone to ensure that there was no one in the house. (I'm a big chicken when Dh is not home)
After sitting on my bed for 10 min waiting, and still no police, I called alarm company back to find out how long. I was not leaving my bedroom as I was too freaked!
They said that they called at 5:02 and it was now 5:09 and that it can take awhile for them to come depending on how busy.

I ended up calling 911 to find out how long, and telling them what happened, and she said she had not log at all for them to come to our house and that she would send someone right over.
The police checked out the place, said all the windows appear to be locked, and no signs of forced entry when walking outside the house. After leaving I tried to reset the alarm, and it wouldn't go on. The only reason that is, when something is either in the way of a motion sensor or a window is open. I checked my bedroom, my daughters bedroom, and then checked the third bedroom. It was only a tiny tiny tiny bit open.. still locked, but far enough to the left that it could be moved to the right a bit and "close" tightly. So not sure if the police man did this when checking, or if this was the attempted point of entry? Also after further inspection this morning when it was actually light out, I see a thumb print on the outside of the window and its a left hand. I tried to take a picture, but my camera would not pick up the print just what was outside, or the reflection in the window.

In either case, freaks the hell out of me, next to impossible to fall back asleep (dd was asleep in minutes)

So what can I do to make it more "Safe". Its only rarely that dh is away for the night but aside from getting a dog...? We have good locks on the windows (so I thought?) and thinking of putting sticks in the windows? There are alarm stickers everywhere. The police thought it was pretty secure and thought someone was not too bright for trying. (if that is what happened)

I am not 100% convienced that someone did try and enter, but in the just over a year we have lived here, this has NEVER Happened so dont know what else it could have been?