it would have been

[navi tasan]

Which are correct:

1) It was possible for the cat to go out, but I don't think it did. I think it is still in the house.
2) It would be possible for the cat to go out, but I don't think it did. I think it is still in the house.
3) It would have been possible for the cat to go out, but I don't think it did. I think it is still in the house.

I think the first two are fine (I prefer '1') but the third one seems incorrect to me. To me 'it would have been possible' implies that if a particular condition had been realized, something would have been possible, but that condition was not realized, and therefore that thing never became possible.

 

[emsr2d2]

I can't say any of them is grammatically incorrect but none of them are natural.

The cat could/might have gone out but I don't think it did. I think it's still in the house.
It's possible the cat went out but I don't think it did. I think it's still in the house.

 

[SoothingDave]

You'd probably use "he" or "she" for the cat, assuming you were familiar with it.