Krzysztof Nieroda then called a family member and told them that he had shot and killed his wife and children before shooting himself in the head with a single gunshot, according to investigators.
The murder weapon was found in his hand when officers arrived at the home around 9:30 a.m., police said.
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Responding officers found Krzysztof Nieroda, Justyna Nieroda and Natalie Nieroda dead at the scene. The 14-year-old was rushed to a hospital in critical condition, but later died of his injuries, officials said.
"In tragedies of this magnitude, there are no words that can heal, nor explanations that can serve to make sense of them to the public," Union County Prosecutor William A. Daniel said in a statement. "Our thoughts go out to the family and friends of these victims and to the Linden community as a whole in the wake of this horrible event."
The circumstances that led to the apparent murder-suicide were unclear.
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"When things like this happen, people are left trying to figure out why, but nobody will really know why," Linden Mayor Derek Armstead told MyCentralJersey.com. "Nobody will know except for them, and they are gone."
Linden Police Chief David Hart urged those who may be suffering to find help.
"We are not alone in our grief; each of us has a shared responsibility to be there for our loved ones as we mourn the loss of our friends and neighbors," Hart said in a statement. "If you or someone you know may be suffering, please don't hesitate to ask for help before a crisis occurs."
Investigators did not immediately provide further information.
Linden is located about 10 miles south of Newark and 19 miles from New York City.