NEW YORK – A man out walking his dog early Tuesday morning made a gruesome discovery: the dismembered remains of a woman in a heavy duty plastic garbage bag, police said.

Hours later, a suspect was in custody, and police said he had made statements implicating himself. His name wasn’t immediately released.

Police believe the victim was 45-year-old Tanya Byrd, a home health aide who was last seen Monday. Her remains were stuffed in four bags and scattered along four blocks, police said. The medical examiner’s office was working to make a formal identification and determine a cause of death.

The first bag was discovered in the Melrose neighborhood of the Bronx at about 5 a.m., when the dog started sniffing at some trash. Among the pile of trash was a duffel bag containing a plastic bag with a bloodied leg inside.

When police arrived, they found three other bags with remains on surrounding blocks. One contained a leg and an arm. In another, a portion of a torso with shoulders. In the third, a head.

Mario Font, a building superintendent, said he saw police open the bag near the pile in front of his building, and the trash bag inside it held a leg. He said he believed it was the right leg, judging from the toes.

Font was disturbed by the scene in a neighborhood he said has improved in recent years. “To chop a person in pieces, it’s a horrific crime,” he said.

Police cordoned off at least four separate locations on the streets surrounding the initial discovery. There were uncollected trash and recycling piles throughout the area, and white sheets covered items near the piles in at least two spots.

Witnesses said the sheets were placed shortly before children and parents started walking through the neighborhood to reach a public elementary school.

Police interviewed witnesses and also were talking to the victim’s son. Some witnesses told police an SUV dropped the bags off sometime during the night.