According to the FAA, this is a privately owned public use airport; I see no indication that prior permission is required (PPR). https://www.gcr1.com/5010ReportRouter/21N.pdf Per...

Mattituck Airport (FAA LID: 21N) is a public use airport situated one nautical mile (2 km) southeast of the central business district of Mattituck, a hamlet in the Town of Southold...