Karen Kuzmak Roche was identified as the child's mother through DNA testing this month, Meriden Police Chief Jeffry Cossette said.
Roche was 25 when the baby boy was found wrapped in blankets on Jan. 2, 1988. Investigators believe the child was left in the parking lot for five days in subzero temperatures before he was found.
Cossette said the case was one of manslaughter, which a 20-year statute of limitations. He said Roche is not expected to face criminal charges.
The department identified Roche through DNA testing that identified her distant relatives and led investigators to her home earlier this month. She said she was remorseful for her actions.
“Miss Roche indicated that she had been waiting 32 years for the day in which police would be knocking on her door,” Cossette said.
Local clergy named the infant David Paul after his death.
Officials said it appeared Roche called the fire department on Dec. 28, 1987 to report something in the parking lot where the infant was found. She didn't say it was a child.
"She made a huge mistake. She probably thought irrationally that someone would find the baby and save it,'' Rev. Ralph Roy, who named the boy, said in an interview with the Hartford Courant years ago, before he passed.
Investigators believe the father, who was not identified, did not know anything about the baby being abandoned.
The Associated Press contributed to this report.