The Crimson Crusader on Dragnet
Yes, there was a costumed character on one episode of Dragnet. That episode aired in 1969.
Amazon Instant Video describes the story as "Sgt. Friday and Officer Gannon search for a burglary suspect dressed in a bright green cape and Napoleon hat who only steals photos of an old comic-strip hero," and Amazon will be pleased to charge you $1.99 to watch that show over here.
But wait! Don't click that mouse! I have found the show for you to watch at no charge. (Your subscription fee to The Hayfamzone Blog keeps paying for itself over and over again, doesn't it?) Here are the first 15 minutes of the episode, and here are the closing 11 minutes. Enjoy!