Ron Zeitlinger of the Jersey Journal reported Lauletta "came close to striking the officer with his vehicle" during the incident.
"We are aware of the situation and are in contact with Kyle," a Giants official told Zeitlinger. "We are still gathering information."
Weehawken Police provided details on the arrest, per SNY:
SportsNet New York @SNYtv
Weekawken Police release a statement on Kyle Lauletta's arrest: "Upon being directed by an officer to continue in his marked lane, Mr. Lauletta attempted to evade him, making an illegal turn and continuing towards Route 495, almost striking the officer" https://t.co/FIBVhkgugt
Ryan Dunleavy of The Star-Ledger noted the backup QB wasn't on the field for Tuesday's practice.
Head coach Pat Shurmur also made a statement on the situation, per Ralph Vacchiano of SNY.
"We were made aware of the situation this morning, and we have been in contact with Kyle," Shurmur said. "We are still in the process of gathering information. This is obviously very disappointing."
New York selected Lauletta out of the University of Richmond in the fourth round of the 2018 NFL draft. He was a three-year starter for the Spiders.
The 22-year-old Pennsylvania native struggled during the preseason. He completed just 48.6 percent of his throws for 194 yards with one touchdown and two interceptions on 35 attempts.
He has yet to appear in any regular-season games while operating behind starter Eli Manning.
With the Giants standing at 1-7, however, Shurmur refused to rule out turning the offense over to Lauletta following the team's Week 9 bye.
"We'll see," he told reporters Monday about Manning's status as the starter.
Alex Tanney is the other quarterback on the New York roster.