Federal prosecutors had accused Shaw of taking $10,000 in bribes from a government informant and proposing the cooperating witness make a $10,000 campaign contribution to an unnamed Jersey City official.
DeFazio said the death doesn't appear to be a homicide. He says an autopsy will determine the cause of death.
Earlier in the day, Secaucus Mayor Dennis Elwell is the first elected official arrested in last week's corruption sweep in New Jersey to resign.
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Secaucus town administrator David Drumeler said he received Elwell's resignation letter Tuesday afternoon, and it was effective immediately. The town's deputy mayor has taken over until a replacement is named, Drumeler said.
Elwell is charged with accepting $10,000 from a federal cooperating witness in exchange for help on a building project in Secaucus.
In a statement released Tuesday, Elwell's attorney, Thomas Cammarata, said his client is resigning because it is in the best interest of his family and the people of Secaucus.
"Those who perceive this action to be an admission of culpability as to the pending criminal allegations are gravely mistaken," Cammarata said.
Elwell, 64, had been mayor since January 2000 and was up for re-election in November. A Secaucus native, he runs a family owned-trucking business that specializes in hazardous material transport. In his resignation letter, Elwell made reference to his combat experiences as a paratrooper during the Vietnam War and the loss of his teenage son who was killed crossing a Secaucus railroad track in the 1980's.
"Dennis will fight with the same intensity and courage that he displayed in these life experiences," his lawyer said.
Drumeler described the mood at city hall as one of "shock and disbelief" that the popular mayor was suddenly out of office. Secaucus, just outside of New York City, is home to about 15,000 residents.
Part of the city is a gritty industrial and trucking corridor that is home to many major company warehouses. Its residential mix of New York City commuters in recently built high-rises and lifelong residents in modest homes with manicured lawns help it retain a small-town, suburban feel in the shadow of Manhattan.
Elwell is the only elected official arrested in the sweep to step down so far, and his lawyer said Elwell will plead not-guilty to the charges.
State Assemblyman Daniel Van Pelt, who also was arrested, was fired from his $85,000-a-year job as administrator of Lumberton Township, a small southern New Jersey town. Town officials have asked federal authorities to review all of Van Pelt's dealings while serving in the post.
In all, 44 people - including three mayors and two state lawmakers - were arrested in an FBI sting that started with an investigation into the black-market sale of human kidneys and fake Gucci handbags and evolved into a sweeping probe of political corruption in New Jersey.
Ridgefield Mayor Anthony Suarez rebuffed a borough council nonbinding resolution passed Monday evening, calling on him to resign. Suarez said during the contentious council meeting that he is confident he will be exonerated. He's charged with accepting a $10,000 bribe.
Hoboken Mayor Peter Cammarano III has denied charges that he accepted bribes and is rejecting calls to step down, which included a large protest in front of city hall Monday evening.
Jersey City's mayor has suspended without pay six employees arrested last week in the probe, including Deputy Mayor Leona Beldini.
Most are charged with accepting bribes from a federal cooperating witness posing as a developer looking to gain approvals for a building project.
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