In a Police Procedural, interviews are short and sweet, and the characters try to give as little useful information as possible. This is done to keep as many of the characters as possible suspects for as long as possible, but often falls flat. In order to give an excuse for this unhelpful behavior, the characters that didn't do it often have a Big Secret. In cases of You Didn't Ask, they'll answer your questions as specifically and as literally as they can, dragging the whole thing out.
One need not be a suspect to be as unhelpful as possible. Almost never, in the entire history of television, has a victim's family been interested in finding the actual perp once a Red Herring suspect has been identified. If a suspect has been wrongly convicted, the family will occasionally go as far as to actively hinder the investigation, even when it is obvious that the real killer is still at large, preferring the "closure" of a conviction. This is one of the rare cases of a cop show mirroring real life.
This trope is sometimes inverted, rather than subverted. The guilty party has been providing information to clear his name, expressing support for the investigation at every opportunity, and generally being too helpful — all in an effort to deflect suspicion. (CSI is fond of this variation, as is Scooby-Doo.) Another alternative is Infraction Distraction, where the guilty party confesses to minor wrongdoing to cover up major wrongdoing.
Note that in real life, doing this is not always a bad thing. Knowing where your rights begin and end and what limitations police officers have in questioning, holding, and searching you, and that you always have the right to remain silent, can save you being unjustly inconvenienced, held, or even mistreated. Of course taking this too far, actively hindering the police,note or wrongly assuming your or their rights can easily land you in cuffs and a squad car. At least for our tropers in the United States, asking "Am I being detained?" is a good question to post to a policeman who's trying to sit on you as it puts them in a Morton's Fork situation unless they have valid legal reasoning to suspect you of a crime,note though asking this in a country without such rules for police officers would probably be a pretty bad move.
See also Perp Sweating, Only Bad Guys Call Their Lawyers, Figure It Out Yourself. Not to be confused with Unwanted Assistance or Bothering by the Book.