Did Florida governor go too far?

Gov Rick Scott just signed a bill that would make it a crime for a doctor to ask a patient if he owns a gun. The NRA backed bill originally called for a penalty of 5 years in jail and fine. I guess their concern is that mentally ill people will be deprived of their 2nd amendment rights. Another article right next to this one in the paper tells of a gunman going on a rampage and killing 5 people.