If you are under criminal investigation by a police department you are under no obligation to inform your employer. An investigation is just that an investigation. Lots of time nothing comes out of a criminal investigation . University of Illinois could have been sued by Terrance Shannon if no charges were filed and they suspended him. If your employer fires/suspended you because you are under investigation by the police for and incident that’s not related to your job and happened outside of work you have every right to sue your employer