I can see why some people think that Capote was in love with Perry, but I didn't see any clue or hint in the book that could suggest that Perry was actually gay, although it is an interesting point of view.
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Dick’s mother makes a comment about Perry that again foregrounds the topic of homosexuality: “I wouldn’t have him in the house. One look and I saw what he was. With his perfume. And his oily hair. It was clear as day where Dick had met him” (169). Although this is not always the determining element of Perry and Dick’s relationship, it continues to surface and inflect the reader’s perception of events. And in this case, it renders Perry a social outcast; whether or not we choose to believe that the men are romantically involved, homosexuality functions as a symbol of Perry and Dick's larger alienation from conventional society.
It is also believed that Perry's homosexual tendencies were revealed via his affections for not only Dick, but by a former cell mate by the name of Willie-Jay as well.