The police are presented as being very professional and intelligent.
The manner in which they speak is very formal.
Dewey mentions that his attitude towards the crime was a "Personal proposition" because his family knew the Clutters. This shows that he has deep morals and wants to bring justice to his friend.
He also mentions that even if he didn't know the Clutters, he would still treat it the same because it was horrific, and unexpected. In Dewey's dream about Perry and Dick, Capote presents them as running away and Dewey not being able to catch them, this symbolises Dewey's frustration at not being able to bring justice to the Clutters fast enough.
Nye's ability to corner the convicts is proven when