(CNN) -- Police said Friday they have received more than 30 leads "from concerned citizens" to help with their investigation into the fatal shooting Thursday of a 13-month-old boy in Brunswick, Ga.
"Our uncompromising search has led us from door to door throughout the area," said Todd Rhodes, a spokesman for the Brunswick Police Department.
Sherry West told CNN affiliate WAWS that she was pushing her son in a stroller at 9 a.m. Thursday when two boys approached and demanded money, then wounded her and fatally shot her boy.
"He said, 'I'm gonna kill you if you don't give me your money,' and I said, 'I swear, I don't have any,'" West said. "I put my arms over my baby and he shoves me and he shot my baby right in the head."
Both boys then ran into a residential neighborhood of this seaside Georgia town some 30 miles north of Florida, she told police.
The woman told reporters that one of the attackers appeared to be 13 to 15 years of age while the other was as young as 10.
Rhodes said police were checking school attendance for students who had been absent on Thursday and fit the descriptions provided by West.
"We are aware there is some speculation being circulated throughout the rumor mill," Rhodes said, without specifying what he was referring to. "However, let me assure you -- as I previously indicated -- that we are thoroughly investigating this case and we will not, I repeat, will not leave any stone unturned."
Asked if West herself was a suspect, he said, "We are not at liberty to discuss the intricacies of the investigation, as it could possibly damage it."
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 was shots that went out in the area," Rhodes said. "Right now, we are not ruling anyone or anything out."
After stating that "there is no clear motive right now," the public information officer was asked about West'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."
Rhodes said crime is not common in the residential neighborhood where West said her child was shot. "It's a nice area, it's a clean area, it's an area where law-abiding citizens not only live, they also work and play.
"Much like every other city in these United States, from time to time we will have a glitch. Unfortunately, this happened here in Brunswick, Georgia."
Asked whether people in the neighborhood should fear for their safety, he said they should be alert and report any suspicious activity. "But no, they have no reason to live in fear," he added.
Meanwhile, investigators returned Friday to the crime scene. "We want to make sure we haven't overlooked anything," Rhodes said.
He said West has been cooperating with authorities.
"But why my little one?" asked Louis Santiago, the father, in an interview on Thursday with WAWS. "You know, you should have just taken the pocketbook and go."
Police have offered a $10,000 reward for information leading to the killer.
"This is obviously just a terrible day in the city of Brunswick," Mayor Bryan Thompson told reporters on Thursday, "and made even more terrible by the senseless killing of a young child. And it appears perpetrated by children themselves."