The husband of a 29-year-old Bethpage special-education teacher found dead in North Hills Wednesday has confessed to choking her to death after the two had an altercation at their home Sunday morning, Nassau police said at a press conference Thursday morning.

Police said Bill Walsh came home early Sunday morning from a trip to Atlantic City and engaged in a verbal dispute with Leah Walsh. The dispute, possibly over his alleged infidelity with one or more women, escalated into a physical fight that ended when he choked her to death, police said.

Cops had been searching for Leah Walsh since Monday, when her abandoned car was found on the Seaford-Oyster Bay Expressway. Investigators say her front right tire was flat with no recognizable tire damage, indicating that the air had been let out of the tire manually.

Walsh?s body was found in a wooded area outside the North Hills Country Club by an employee of the club, police said. Bill Walsh dumped the body at the location at about 9:30 p.m. on Sunday, after he did laundry and went to McDonald?s, possibly to help establish an alibi for the murder.

After her body was recovered, Bill Walsh was arrested by homicide squad detectives and he later confessed, police said.

Walsh?s attorneys say their client was coerced by police into giving a confession.

?He was in custody for over 15 hours, sleep deprived, the inability to speak to family, friend or lawyers, and in fact, they used trickery and deception to get him to say the things they say he said,? says attorney Karl Seman.

According to detectives, Walsh?s seven-page confession came after six and a half hours of questioning.

Walsh has pleaded not guilty to second-degree murder charges and is being held without bail.

Family, friends, colleagues mourn loss of Leah Walsh