Some officials fear it could lead to lawsuits.
The monument would include a two-ton section of a steel beam from the World Trade Center with a cross carved into it.
It's apparently a remnant from the recovery effort at Ground Zero. Welders would cut crosses from beams and place them in the stretchers of fallen firefighters and police as their bodies were carried out.
"We didn't take this piece of steel and carve out the cross ourselves. We didn't ask for it to be there. This is the way this steel came to us," said Princeton Dep. Chief Roy James.
James is leading the effort to place the beam at a memorial near the old borough hall.
But, local officials are worried that the cross on it may violate the separation between church and state.
"We have our attorney looking into if we would be open to litigation for this and what the risk is," said Mayor Liz Lempert.
"As a Jew it doesn't bother me," said Dep. Chief James. He also said he disagrees with the suggestion to turn the cross from public view when the beam is installed.
"If we take that away, if we hide it, we don't show that - number one - we are taking out history," James said.
Number two, said James, it disrespects the memory of almost 3,000 people who died at the World Trade Center.
Some others around town agreed with James.
"If that's part of the World Trade Center, I feel like that should be honored in some way and if that's part of it and it should be put up," said Danielle Moscato of Staten Island.
"It would not bother me but I do understand how it could raise a concern for some people," said Octavia Gurley of Princeton.
Deputy Chief James said he would like to have the beam in place by this coming September 11th but, with the controversy continuing, he's not sure that will happen.