Sounds like some kind of cat.  I see by the picture you chose for the article that you had already come to that conclusion.

When I was a girl our housecats did a lot of hunting and both the biting the head off thing and the displaying the kill thing sound very familliar.  

A full grown possum sounds like awfully large prey for for a housecat, though the habitat you describe behind your house sounds like a perfect place for a feral cat to live.  Maybe the possum was injured and the cat finished it off?  Or maybe it's a huge specimin of a housecat.  Some breeds do get quite large.  I'm not sure what breeds of wildcat live in Texas.  Do you have lynxes or something?

Either way, it wouldn't be dangerous to humans unless you tried to catch it or something.  Just enjoy the idea of a tiny tiger hunting the jungles and grasslands of your home territory and be happy that it's much too small to consider you prey.

Karas

My wife said we should contact Animal Control and have them bring around a cage or trap to catch it. But I said no.

Frankly, I think the whole idea of a large wildcat roaming around here is very cool.

And you're right: no-one is going to get hurt by  it. Aside from small animals. But that's just nature. So, I'm cool with it wandering around and maybe one day I'll get lucky and get a picture of it.

A predator that seems to be mainly interested in eating large destructive rodents sounds like like a blessing to me.  Probably a bobcat or a really big feral domestic cat.  Both are plentiful in North Texas.  I agree that a coyote is possible, but highly unlikely.  If it were a coyote, the local pets would be disappearing in addition to the large rodents.  The climbing involved clearly points to a feline. 

Though possums look ratlike they aren't rodents.  They are marsupials, the only species of marsupial native to the americas.

Sorry to be pedantic about it but I used to be a professional naturalist.

Hey,

This is scary, I used to live in Arlington. I live in Mansfield now.

Perhaps you can get me more details to the story? If you want my email let me know in the comments Nick.

Think that creature has relatives in Northern California. I live in the Sierra Foothills and have seen numerous small animals with the head missing. We also notice a strong feline urine stinch on and around the deck periodically.

On 10/2/11 I was getting dog food on the side of the house in the early evening when it began to "rain" on me. I hurried to the deck so it wouldn't wet the food. It was only after I walked up the steps to the deck I realized the only rain was where I was standing. I went in and got a flashlight to be sure I was correct. I was, the only wet area being where I was standing. It was a clear starry night.

It wasn't until I went inside again that I discovered the "rain" was actually feline urine! I was soaked. The only reasonable thing I can assume, since there was nothing overhead where I was standing, is a mountain lion must have sprayed me from the roof on my house - 10 feet away.

Jon:

There's not much more, if indeed anything else, to add right now. The article covered everything that has happened so far. But, if there are any more developments, I'll definitely post something in the Comments here.

Nick