I suspect Penguin has done his civics homework well and has discovered that Paragraph 34-A of the city charter has never been officially repealed. It specifically allows convicted criminals to run for public office.
15 seconds sound clip from Batman (1966) - Hizzonner the Penguin (S2E17) TV Series.
You can hear this line at 00:04:30 in the Blu-ray version of the movie.
Quote context
[...]
- Civics will have to wait, Dick. Penguin is up to some new tricks.
- Alfred, you may exercise your familiarity with the Bard.
- Did you hear those rumors in the lobby? The Penguin running for mayor.
- It won't be if he's elected.
- Besides, I thought convicted felons were barred from holding any official office.
- I'm glad you two are here, Dynamic Duo. I wanted a chance to say goodbye.
- I think you tend to overestimate the Penguin, Mayor Linseed.
[...]