“I would think certain village area residents would be reluctant in the beginning,” Mr. Aube said. “I think it would probably be an easier sell for larger departments, like Southampton Town and Riverhead Town and East Hampton Town.”

At least one village is content, for now, under Southampton Town Police coverage.

While Sagaponack Village had some issues with Southampton Town’s lack of police coverage in spring this year, Mayor Don Louchheim said the town has taken productive strides in improving its service this summer.

Mr. Louchheim noted that in the spring, he had complained to town officials about the lack of police coverage, given the high taxes that the wealthy village pays. Although the issue of taxes have not been resolved, Mr. Louchheim said police coverage issue has been “satisfactorily answered” with an increased number of traffic control officers, and a bumped-up police presence on Monday nights to address parking and speeding in beach areas. The town also assigned a liaison, town police officer Melissa Elliston, to meet twice a week with the village to identify any problems that might surface.

Originally, Mr. Louchheim said the village was considering “divorcing” from the town and forming its own police force. While that option is not yet off the table, Mr. Louchheim said Ms. Throne-Holst has done a “good job” in addressing the village’s concerns.

“We’re still exploring,” Mr. Louchheim said. “If we were to do it, what would the cost be, and what would the benefits be. But what I’m saying is one of 
the key factors for us doing this has now been eliminated. 
And we are very appreciative of the efforts of the Town Police since we raised the issue in the spring.”