The family is suing the home's previous owners for not telling them about it before the sale, claiming they had received letters too.
In letters "the Watcher" wrote that the home "has been the subject of my family for decades."
"I asked [the previous owners] to bring me young blood," the Watcher wrote.
Content from the letters are included in a complaint filed to a New Jersey Court. The house is worth $1.3m (Â£826,131).
The stalker wrote that he has been in control of the house for two decades and he asked the previous owners to sell it.
"You have changed it and made it so fancy...it cries for the past and what used to be in the time when I roamed its halls," the stalker wrote. "And now I watch and wait for the day when the young blood will be mine again."
Westfield mayor Andy Skibitsky, speaking at town hall meeting in Westfield on Tuesday, said "The Watcher" is a mystery, ABC News reports.
"When, over a year ago, this matter was reported to the police, our police department conducted an exhaustive investigation," Mr Skibitsky said. "Such efforts, however, have not yielded information leading to charges being filed and, therefore, this case is pending introduction of any new evidence."

The police said a car was set on fire in Main Street, Crumlin, between 03:20 BST and 03:40 BST on Saturday and the blaze spread to the takeaway.
Residents from flats above the takeaway escaped without injury. Other premises on the street have been damaged.
The police said, at this stage, they were not treating the incident as a hate crime.
SDLP councillor Thomas Burns said it was unclear what had actually happened but it looked like the car had been rammed against the shutter of the restaurant.
"This is an absolute disgrace," he said.
"Whether this vehicle has been moved or burnt and has been rammed against the shutters of this takeaway, for the people living upstairs, it could have been an absolute disaster.
"If the blaze had got going, if the people had not got out, the smoke could have killed them, never mind the fire.
"I'm horrified that these Chinese people have been targeted. Why it was them, is a question that is being asked."
Councillor Mervyn Rea of the Ulster Unionist Party said: "That vehicle could have exploded, it could have caused damage where it was parked, it could have caused injury to anyone on the street and, equally so, when it propelled into the shop and set the shop ablaze.
"It could have caused a nasty accident when it was veering across the street."
Anne-Marie Logue, Sinn FÃ©in councillor, said people in the area were "aghast as to why this has happened".
"We are very annoyed for the business involved as well and the family are devastated," she said.
"It's obviously put them out of business for quite a few weeks.
"Opportunists decided to break into the car. The car was put on fire and unfortunately it was directed towards this shop. I'm just glad that nobody has been hurt."
She said Â£700,000 had recently been invested to upgrade Crumlin Main Street.
The police are treating the incident as a suspected arson attack and have appealed for information.
A New Jersey family will not move into their new million-dollar home after receiving threatening packages from a mysterious sender called "the Watcher".
[NEXT_CONCEPT]
A Chinese restaurant in County Antrim has been destroyed in an arson attack.