Thanks for your responses. I was thinking about that solutions as well. But before he changed his clothes he was barefoot, and then again after changing for second time. And also it seemes that he takes off the pyjama. So the only thing I can imagine is that the feather could stuck only in his hair or something like that. I like this episode a lot but that thing always bothers me a little while watching.
I think it was Columbo that brought the feather, he was at the crime scene and was holding the thorned pillow.
Although Columbo should have thought that instead of suspecting a patient imo.