On Tuesday, Curran vetoed a bill to permit the county to sue on behalf of individuals who say they have been harassed, menaced or injured stemming from their status as a first responder.
On Thursday she said she fully supports the first responders but called the bill "flawed."
"The concern is that it could open up the county to a barrage of lawsuits and at the end of the day I have to make the decision in the best interests of our county," Curran said.
Republicans in the Nassau Legislature are considering how to override her veto.
Curran says she respects the democratic process and will address that if it happens.
Civil Rights activists argue the bill is payback for last year's demonstrations against police brutality, and would violate free speech.
ALSO READ | Census: NYC population surges to 8.8 million with almost all growth in cities
* More Long Island news
* Send us a news tip
* Download the abc7NY app for breaking news alerts
* Follow us on YouTube
Submit a News Tip