The lone survivor of the shooting spree is recovering at University Hospital in Columbia, Mo., CBS News correspondent Cynthia Bowers reported.
Police are seeking a 23-year-old backhoe operator they're not yet calling a suspect, but who may have been involved in disputes with the dead.
Some 70 officers are looking for Joshua Maylee -- who's being called a "person of interest" in three shooting deaths.
Sgt. Robert Bruchsaler, of the Mid-Missouri Major Case Squad, told CBS News, "The person we are looking for is not randomly going out and shooting people. These were targeted individuals."
Bowers reported it's believed Maylee may be trying to settle scores with people and that's led police to issue a chilling warning to anyone who may have had problems with him in the past.
Bruchsaler warned, "We would ask that you leave your residence if he knows where you live. We would ask that you leave the area with your family and go someplace of safety that you know he wouldn't get to."
Eugene and Jackie Pinet were killed near the town of Tibbets, Mo., while Jeffery Werdehausen died in nearby Holts Summit.
A fourth shooting victim, Werdehausen's wife, Gina, was taken to University Hospital in Columbia in critical condition. The hospital was put under lockdown in case the shooter showed up there.
Matt Splett, University Hospital spokesman, said, "We have security personnel at every entrance screening people to ensure the safety of those people inside the hospital."
Like a modern version of the game telephone, news of the hospital lockdown became rumors on Twitter of a gunman loose on the University of Missouri campus.
Police don't know where Maylee is, but they believe he may be driving a silver Pontiac Bonneville. And, they say, he should be considered armed and dangerous.
Bowers said, "His mother, Jackie Cook, told a local newspaper she hasn't heard from her son but prays the allegations against him are not true. Problem is, there was a witness to this attack. She says the gunman shot a woman outside, then came inside the house to find her husband and kill him."
Criminal profiler Pat Brown said on "The Early Show" the warning about Maylee should be extended to more people.
"It is kind of an unusual warning, it's a good warning because, clearly, he targeted four people he had problems with. But I'm concerned it doesn't go far enough," she said. "They are saying he is armed and dangerous but now a spree killer, two sets of people at two different locations, he's on the run and armed. There is no reason for him not to take somebody else out if he needs their car or money. He's got to survive somehow, and he is angry. I would say they should issue a larger warning to the entire area and the state, anywhere this guy could be coming after you next and could be for something he just needs."
"Early Show" co-anchor Maggie Rodriguez said, "He's already killed three people. Which means he knows if he's caught, he's going to go at the very least to jail for life, if not worse."
Brown agreed, saying spree killers often become desperate.
She explained, "They know there is no place to go, but run and hide and have to run on the road unless they have someone to harbor them like a family member unless they get to the border and cross it. They will run out of money. We've seen other spree killers that have shot people for their cars and gone into their homes and stolen money from there or hidden there. I would say, get that warning to everybody, this guy is extraordinary dangerous, not just if he has an issue with you."
Rodriguez asked Brown, "If there is a witness, why are they calling (Maylee) a person of itnerest instead of a suspect?"
Brown replied, "That is odd, but today the word they use, 'person of interest.' I think it is the legal team saying, 'Don't call him a suspect unless we have of absolute proof of that. Just say 'person of interest.' We all do that, saying 'person of interest' although we are thinking he's the suspect."
So what would make a person snap like this?
Brown said, "Well, he certainly has some, you know, issues in the past. We know he have a couple of felony charges against him for theft. Clearly when he wants something he goes and gets it. Apparently, these people didn't do what he wanted them to, and that created rage in him, so we're talking about a severe psychopathic disorder here and makes him, again, very, very dangerous because he has obviously no particular concern for other humans. He thinks he's right and has the right to take out his vengeance on anybody for whatever reason."
Brown says she suggests people who live in this area stay vigilant.
"I'd certainly be on the lookout for him and lock my doors carefully at night and make sure I don't see a car coming up my driveway I don't know. Don't open the door and any circumstances you absolutely do not know on the outside, just really keep your eye out for him," she said. "The police need to find where he is so I'm hoping the eyes of everybody will go out there, not just people who have some particular -- he's had some particular beef with -- it should be everybody."