Josue Chinchilla and Michele Callan are suing their landlord for the return of the $2,250 (£1,397) deposit they put down upon moving into the house in February.
The couple said that shortly after they moved into the house they heard mysterious sounds from the basement, while lights switched on and off by themselves and items stored in cupboards ended up on the floor.
They also reported that an "unknown force" tugged at Chinchilla's bedsheets, and Callan saw a dark apparition in the bedroom.
The landlord, Dr Richard Lopez, has filed a countersuit, and his attorney has suggested that the couple's story may be a ruse to avoid paying rent they can't afford.
Lopez's attorney told the Ashbury Park Press: "Frankly, there is something else going on. She is a single mum, she has this fiancé living with her. I think she is in over her head and she can't afford the rent.
"She needed to show her ex, the father of her kids, that she has a good place for them to live."
Prior to moving out, the couple called in the Shore Paranormal Research Society to investigate the supposed paranormal activity. Cameras and recorders were set up, and captured some strange occurrences (including bowling pins falling over by themselves, and the sound of laughter in an empty room).
Asked whether he believes the house to be haunted, the society's manager Nick Carlson said: "Haunted? No, I do not think so. Do I think there's stuff paranormal going on there? Absolutely."
The couple have since moved into a motel, describing the saga as "a horrific nightmare".
View investigative footage of the house - courtesy of the Shore Paranormal Research Society - below: