Many times throughout the series, Jessica Fletcher will ask the police (such as the local Sheriff's and homicide detectives) to find and bring in suspects and witnesses to the station for interviews, even though it's pretty clear that the people she wants to interview don't want to come in voluntarily. If there is no probable cause for an arrest or an active arrest warrant, the police can't make a person go anywhere against their will. Once in a while, a wealthy or educated person will assert this and ask a lawyer to be present, but this is rare.
Jessica Fletcher often undertakes actions which would result in evidence and investigation being compromised. Since she is only a crime novel writer and has never been a police officer, these actions could result in cases being dropped or overturned upon appeal. There is no way that the local District Attorney would allow her to perform the actions that she does.
In multiple episodes, Jessica Fletcher manages to obtain a "confession" from murder suspects in their own homes, explaining how she uncovered the truth. In reality, this would be a gross violation of police procedure, as revealing evidence outside of an official interrogation or plea negotiation is improper. Even though Jessica is merely a mystery writer with no formal law enforcement training, she often confronts the murderer in the presence of a local sheriff or homicide detective-who, in real life, would be obliged to tell her that such actions are illegal.