CNN — BRUNSWICK, Georgia (CNN) -- A woman says she was taking her 13-month-old son for a walk in this Georgia town when they were approached by two boys who demanded money, then fatally shot her boy and wounded her.
"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,'" Sherry West told CNN affiliate WAWS. "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.
Police responding to a 911 call found the baby shot dead and his mother with a leg wound.
The mother told reporters she was pushing her son in a stroller around 9 a.m. Thursday when she was approached by the two boys. One appeared to be 13 to 15 years of age while the other was as young as 10, she said.
Authorities were checking attendance records Friday at schools in an attempt to identify suspects.
City Manager Bill Weeks said no other witnesses have come forward.
"But why my little one?" asked Louis Santiago, the father, in an interview with WAWS. "You know, you should have just taken the pocketbook and go."
No weapon has been recovered, Police Chief Tobe Green told reporters.
Police have offered a $10,000 reward for information leading to the killer.
Asked about what angles authorities were pursuing, police spokesman Todd Rhodes said, "Anything and everything."
"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."