"We have no indication it's true or not true," said Capt. Gary MacNamara, adding that authorities had not received a complaint about the neighbor before the killing.
Jonathon Edington is accused of stabbing neighbor Barry James to death on Monday after his wife told him that James had inappropriate contact with the child. He was released from jail on $1 million bond Wednesday.
"The daughter gave the mother information which was alarming and disturbing. The mom relayed it to her husband. That was the spark," said Edington's attorney, Michael Sherman.
Police said Edington, 29, climbed through James' bedroom window and stabbed him nearly a dozen times in the chest. James' 87-year-old mother discovered his body.
Police had gone to the neighborhood before, when Edington called to complain that he could see James through a window, police said. "Either he was partly clothed or revealed parts of his anatomy that were inappropriate," MacNamara said.
A picture of the two men began to emerge on Friday.
Edington, a graduate of Syracuse University and Fordham University Law School, was described as a quiet man who worked for a small law firm. But the murder charge wasn't his first brush with the law.
The New York Times reported that in 1998, Eddington was charged with harassment and disorderly conduct for throwing items from a Planned Parenthood display at a health fair in upstate New York.
After destroying the display, Edington told a Planned Parenthood representative, "How many babies have to die?" and "How's your conscience," the police said, according to the Times.
Eddington's slain neighbor was described as a troubled man who battled alcoholism. Barry James served two days in prison in May 2001 on a drunken driving charge, according to the state Department of Correction.
"He had some bizarre behavior over the last month," Darrell Maynard, a neighbor, told the Times. "He drove his car through his garage, hit the other neighbor's building."
Pat Wysocki, a neighbor who has known the James family for 39 years, described James as a "very nice fellow" who worked for a funeral home and said she found it hard to believe he would molest a child.
"But then again, you don't know," she said.