COLUMBIA, S.C. — Cadaver dogs looking for a South Carolina boy searched his mother's car and home as she sat in jail on charges of lying to police about what she did with her son, though authorities were not saying whether they found any evidence the toddler was dead.

Despite the grim search, authorities tried to stay optimistic about finding Amir Jennings alive, but the case was getting harder to solve as time goes by. Amir's grandmother said she hasn't seen him since Thanksgiving.

The boy's mother has told police conflicting stories about her son, saying he was with friends and family in the Carolinas and also Georgia, authorities said.

"I'm really just focused on making sure that Amir is OK, or has some harm come to him?" Columbia Police Chief Randy Scott said. "That's what we don't know. That's what we cannot find out."

Amir's grandmother contacted police in early December, saying she was worried about the boy and her daughter, a former Winthrop University student who struggled with depression and had begun acting erratically since her son's birth.

Police say they began looking for Zinah Jennings, 22, but also considered that relatives said she had repeatedly left town for days at a time, taking her son to visit friends in neighboring states.

"The grandmother told me specifically that, when she was in school, she was a very good person, a very good student," said Scott, adding that relatives had filed several previous missing persons reports on the mother. "But once the baby was born, the conduct kind of changed."

Several weeks later, on Christmas Eve, police investigating a one-car wreck just blocks from Jennings' home were surprised to find the driver was the young mother they'd been looking for. Interviewed at a hospital, police say Jennings immediately began giving conflicting statements about where the boy was.

"First it's, 'He's with my sister in Atlanta. Oh no, I'm sorry, he's with my friend in Charlotte,'" he said. "It's all over the place. ... Everything she's telling us is just lies."

Police spoke with Amir's father, who told them he had seen the boy during Thanksgiving but generally has had little contact with him. The father was not identified by police.

After several dead ends, the mother was arrested Dec. 29 and charged with lying to police about her son's whereabouts. Authorities say they have stepped up their efforts to find the boy and are hoping a tip line will yield some information.

"I'm trying to stay optimistic about this," Scott said. "But short of being optimistic, this case bothers me."

Police did not know if Jennings had an attorney. On Thursday, the woman's mother said the family was planning to speak out and would issue a statement, although nothing was received by late afternoon.

Scott said he's struggling to remain optimistic that Amir will be found unharmed. He would not discuss any evidence police have collected from the mother's home or car.

"It's the way this whole case is playing out," Scott said. "It's more than just that the child is missing. The mother is lying about the whereabouts of the child."

There was no answer Wednesday at the blue, two-story home where police say Jennings, her mother and son live, its door and front porch still festooned with Christmas decorations. The house, just a few blocks from one of Columbia's busiest thoroughfares, is on a quiet, tree-lined street of other one- and two-story homes, some with fenced- in yards and porches.

"We see each other and speak and say hello," said Selwyn Young, who lives across the street from the Jennings family and said he recalled seeing Jennings pushing the baby around the neighborhood and walking the family's dog. "Hopefully they find him. Hopefully they get it right."