The Nassau County District Attorney says Joseph Horner lived in an upstairs apartment in the same home as the victim.
He allegedly asked his sister-in-law, Victoria Castle, to help him move a piano in his apartment.
Once there, prosecutors say he attacked the 25-year-old victim from behind and placed her in a chokehold until she was unconscious.
According to prosecutors, he then sexually abused the woman, changed his clothes and called the police.
"The male caller requested police and an ambulance to this location for a deceased female," Det. Lt. Daniel Steller, deputy commanding officer of the NCPD Homicide Squad, said.
Horner waited at the scene for the police to arrive.
CPR was administered, and the woman was taken to a nearby hospital, where she was pronounced dead, police said.
The 27-year-old's wife was at a bachelorette party at the time of the attack, police said.
"He's married, he has been married for 3 years, and his wife was not home at the time of this incident," Steller said.
Horner is an elementary school music teacher.
Oceanside School District released a statement saying in part, "This staff member has been placed on administrative leave effective immediately, pending further review. We have no further information at this time."
"He's an Oceanside teacher, he's tenured, he's very well loved by his students and his colleagues; these allegations are not very in line with what his community friends and family believe," attorney Gregory Grizopoulos said.
Horner pleaded not guilty to murder.
It was very emotional, as Castle's family cried and hugged one another in the courtroom.
She was a student in the process of getting her PhD at Stony Brook University.
Horner's family was also present, and neither wanted to comment on the allegations.
Horner was held without bail, and if convicted, he faces 25 years to life in prison.