The Maniac is an alter-ego of SpongeBob who he does not realize he is.
The police only make a sketch of him. It looks like the only yellow-colored sketch of SpongeBob seen on the show's logo. His design is very similar to SpongeBob, except he has no pores and no pants or undershirt.
In the episode, SpongeBob, as a hall monitor, learns of the crimes caused by the maniac tries to track him down, not knowing that he is looking for himself the entire time.
The police meet Patrick Star who is given a poster of the maniac and matches him with SpongeBob.
However, Patrick's low intelligence doesn't allow him to see they are the same person so he continuously misinforms SpongeBob that the maniac will attack him as the latter goes with it. After causing enough destruction, SpongeBob obtains a poster and realizes that he is the maniac.
When Police arrive to take him in, Mrs. Puff appears and scolds SpongeBob for his destruction of the city and his foolish actions, to his sadness. SpongeBob isn't arrested since Mrs. Puff (accidentally) takes responsibility for his acts but promises to punish him after she is released in six months.
The police may have been referring to the Open Window Maniac, but they said that he was also responsible for car wrecks.