(CNN) — The case of a 13-month-old boy shot dead in his stroller in this waterfront city in southeast Georgia left authorities groping for more leads Friday as they searched for the killer.
"Right now, we are not ruling anyone or anything out," said Todd Rhodes, a spokesman for the Brunswick Police Department.
Police have offered a $10,000 reward for information leading to the killer and have received more than 30 leads, he told reporters.
"We are thoroughly investigating this case and we will not, I repeat, will not leave any stone unturned," he said.
The baby was shot with a handgun, which has not been recovered, he said.
Though no one has reported seeing the shooting, several people called 911 after hearing it, he said.
"What we heard was that there were shots that went out in the area," Rhodes said.
Sherry West told reporters that the incident occurred at 9 a.m. Thursday. As she was walking home from the post office, pushing her son Antonio in a stroller, she said, she saw two boys.
"A boy approached me and told me he wanted my money, and I told him I didn't have any money," she said. "And he said, 'Give me your money or I'm going to kill you and I'm going to shoot your baby and kill your baby,' and I said, "I don't have any money and don't kill my baby.'
"And he tried to grab my purse and I tried to tell him 'I don't have any money' and then he shoved me and he shot me in the ear. It grazed my head," she said, pulling her left ear forward. "And then he shot me in the leg and I didn't feel it. It got numb. I thought it was just a BB gun because it was a small gun."
She continued, "And then, all of a sudden, he walked over and he shot my baby in the face."
West said she tried to perform CPR on her son and that the police took over when they arrived, but to no avail. "We lost him," she said.
During the incident, the smaller of the two boys was hiding behind the larger one, she said. "I don't know whether it was his brother or a friend."
West said she hopes the boys will receive the maximum sentence possible. "If they can use a gun like an adult, then they can be charged like an adult," she said. "I want to see lethal injection or at least life in prison. This child did nothing to him. He was innocent and helpless."
She described the shooter as an African-American, skinny with "a little bit of protruding eyebrows."
She urged residents to be on the alert. "If you see anybody like that, be careful. That's what I'm saying to everybody out there because he may still be in the area."
Asked whether people in the neighborhood should fear for their safety, police spokesman Rhodes said they should be alert and report any suspicious activity. "But no, they have no reason to live in fear," he added.
After stating that "there is no clear motive right now," Rhodes was asked about the mother's account of having been asked for money.
"That is what the mother said," Rhodes said. "We as law enforcement, we can't go off of what anyone says. We have to thoroughly investigate this case."
"This is obviously just a terrible day in the city of Brunswick," Mayor Bryan Thompson told reporters Thursday, "and made even more terrible by the senseless killing of a young child -- and it appears perpetrated by children themselves."
The city's website describes Brunswick, with a population of about 15,000, as "one of the most unique, historic and visually stunning places in the world." It boasts 19th century Victorian-style homes, century-old oaks and magnolia tree-lined streets.