Yeah...dogs are like that...they will blame it on the cat if they think they can get away with it, and they can because they have really cute and innocent facial expressions, cats, not so much, they pretty much always look like they dont know what you are talking about ... conversely, a cat will pin anything bad on a dog, and make it believable..
Cats are smart and independent, a dogs false sense of loyalty to his perceived "master" trumps its long term strategery and intellect!...cats really dont have a "master" in case you havn't noticed, they are in it for themselves! so if you want to really find the true culprit, look at the cat first...Cats are so smart, way smarter than us, and dogs too...they probably already have your Credit carded maxed at Petco and tickets booked on Allegiant to Cancun, ready to go, so be careful!
Dont worry about your house key too much, dog or cat...no big deal, all that will happen is one of them will let their friends in to ransack your fridge, and blame it on the other guy, its more of a trophy and game they play between themselves and us than an overt effort of stealing all your stuff, plus, neither has an opposible thumb, so unless they have groomed some reprobate opossum that lives out in the garage as an accomplice, you have nothing to worry about .....That said, its the cat most likely, and you gotta big problem!..keep your car keys close, check your bank account etc...cats think long term payoff, dogs are all about immediate gratification..
Back in the early 80's, Before I was a Christian, I once lost a Plymouth Volare to a danged old orange marmalade named Alvin, along with my paycheck, and he tried to leave evidence that either myself or Louie the golden lab was to blame! I told the Wife neither Louie or I know how to play cards...and that we were out fishing together that day...She looked deep in Louie's eyes and decided he was not lying...as for me, not so much, but Louie saved my butt like any good dog is supposed to do,
and Alvin was never seen or heard from again...
Mud
They probly took it outside,where we will find it in the spring......