Indeed. As I understand it (ianal), insanity is a positive defense, meaning that you have to prove to the judge/jury in court that you were insane, i.e., that you were functionally incapable of distinguishing right from wrong at the moment you committed the crime. This is because a mens rea, or guilty mind, is necessary to establish guilt and thus criminal culpability, in addition to the actus reus or the criminal deed itself; you have to be in a state where you know, or could/should have known, not to do what you did. Proving a negative, especially when it comes to this, is extremely difficult. You will have to undergo an extensive psychiatric evaluation by a psychiatrist and they have to come to the very strong conclusion that you were well and truly out of your mind at the time of the commission of the crime. Otherwise, just the evidence that you did the crime is enough to establish guilt.

Oh, and if you somehow successfully plead insanity, you will spend quite possibly the rest of your life in a mental institution instead of prison, which isn't much better.

And yes, it's good to remember that police procedurals are to criminal justice what Hackers (1995) is to hacking: a lot of stuff is distorted to make good cinema/television. In the UK, judges on cop shows use gavels (that is strictly an American custom); how can we expect them to get the details of rare events like an insanity defense right?