Story highlights Zimmerman is "doing well," "feeling much better than being in" jail, his lawyer says

He is "on his own" with no special protection, shuttling between locations, he adds

The city police chief's offer to resign was rejected Monday by Sanford city commissioners

Zimmerman pleaded not guilty Monday in the shooting death of Trayvon Martin in Sanford

City commissioners in Sanford, Florida, voted Monday to reject the proposed resignation of their embattled police chief, who has been under fire for the handling of the probe into Trayvon Martin's death in February.

Chief Bill Lee has been on paid leave since March 22, a day after the commission expressed a lack of confidence in him because of the case. He remains so after the commission's decision, with Capt. Darren Scott continuing to serve as acting chief.

George Zimmerman, who has said he killed the 17-year-old Martin in self-defense, was not arrested after being questioned by police the night of the shooting. Arrested weeks later after a special prosecutor was assigned to the case, he was released from jail early Monday and hours later entered a not guilty plea.

Earlier Monday, the city announced in a statement that a separation agreement had been reached with Lee to resign. If it was approved by the City Commission, it would have taken effect at midnight.

But by a 3-2 vote, the commission opted not to accept the proposed deal, which would have permanently dismissed Lee from the job and given him a severance package. Two commissioners had questioned the fairness of Lee losing his job, while Mayor Jeff Triplett said he preferred to wait possibly several months for the results of an investigation into Lee and his department.

"I'm not ready to have him come back and run the Police Department, but I don't know if I'm ready for this either," Triplett said, who sided with the majority to reject the resignation.

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Benjamin Crump, a lawyer for Martin's family, criticized the commission for not letting Lee step down.

"Sanford residents deserve quality leadership in law enforcement who will handle investigations fairly for all people," he said. "If Chief Bill Lee recognized that his resignation would help start the healing process in Sanford, city leadership should have accepted it in an effort to move the city forward."

City Manager Norton N. Bonaparte told CNN that "moving the city forward" is a priority, and something that he hoped might have been expedited by making Lee's departure final.

During Monday's meeting, Bonaparte explained that he and Lee had "agreed to" the resignation, after Lee "decided that he can no longer serve as police chief."

But Randy Jones, a commissioner, pointed to other parts of the agreement stating Lee was "willing, ready and able" to remain on as chief, hadn't been found to have done anything wrong and was resigning on Bonaparte's "recommendation."

Added Patty Mahany, another commissioner supportive of Lee, "What did the chief do wrong? I mean, tell us."

Bonaparte said an interim chief -- in place of Scott, the current acting chief -- could be in place early next week.

The case has drawn intense media attention, with Sanford residents and many civil rights leaders from outside central Florida criticizing the Police Department for not immediately arresting Zimmerman, 28, after he shot the unarmed teenager.

Zimmerman is now free and awaiting trial, after making bail and leaving the John E. Polk Correctional Facility in Sanford at 12:05 a.m. Monday.

"He's doing well. He's very glad to be out, trying to get settled in, still worried about his safety ... talking to his family and feeling much better than being in (jail)," his lawyer Mark O'Mara told CNN later Monday.

Also Monday, O'Mara filed documents in court in which Zimmerman entered a written not guilty plea and waived the right to appear at a formal arraignment.

Zimmerman is now "on his own" with no police protection or security detail, O'Mara said, shuttling to and from several secret locations in light of threats against him and his family. He wore a bulletproof vest while leaving the jail accompanied by Michael Smith, the owner of Magic Bail Bonds.

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"There's been a lot of chatter lately about his release, and that's concerning to him and us," said O'Mara.

The Seminole County Sheriff's Office said that Zimmerman had been fitted with a GPS monitoring device, allowing authorities to track his location.

Zimmerman's release came as something of a surprise. Over the weekend, his lawyer had said Zimmerman might remain behind bars until the middle of this week as his team worked to secure funds to meet the $150,000 bail set last Friday.

With the 10% cash payment customarily made to secure bond, Zimmerman's family needed $15,000 for him to make bail.

Martin's family wasn't pleased by news of Zimmerman's release, said one of their attorneys, Daryl Parks.

"It's tough for them to see their son's killer walk free again," he said.

The case has riveted the nation and sparked intense discussions about race, gun control and "stand your ground" laws, which make it legal for people to use deadly force when they feel a reasonable threat of death or serious injury.

Although details of the shooting remain murky, what is known is that Martin ventured out on February 26 from the home of his father's fiancee in Sanford and went to a nearby convenience store, where he bought a bag of Skittles and an Arizona Iced Tea.

After spotting him, ZImmerman called 911 to complain about a "suspicious" person in the neighborhood. In the call, the neighborhood watch volunteer said he followed Martin after the teen started to run, prompting the dispatcher to tell him, "We don't need you to do that."

Zimmerman claims the unarmed teen attacked him, before he fired his gun. Martin's supporters say Zimmerman targeted Martin because he was black.

On Friday, Zimmerman's father testified that when he saw his son the day after the shooting, he was wearing a protective cover over his nose, his face was swollen, and he had two vertical gashes on his head.

Martin's family and the special prosecutor appointed to investigate the case have rejected Zimmerman's self-defense claim, saying they believe Zimmerman disobeyed the police dispatcher who advised him to stop following Martin, racially profiled him and unjustly killed him.

The case has also shined a hot spotlight on the city of Sanford, and particularly interracial relations in the community.

Mahany, for one, said Monday that reports of gaping rifts in Sanford along racial lines have been vastly overstated, adding, "I don't think Sanford needs healing."

And Jones, the other dissenting commissioner, blamed outsiders for fanning the flames.

"It is not Sanford residents who created this firestorm," he said. "It was brought in from the outside. We all know it."