The unidentified man was also charged with criminal possession of stolen property in connection with the incident, police said.
Because the suspect fled toward Chestnut Ridge, which is just over the border in New York, Ramapo police stepped in to assist their New Jersey colleagues.
The man was stopped on Route 45 and arrested, Ramapo police said.
Police did not specify what the alleged act of lewdness entailed or the thing that the suspect supposedly stole.
Ramapo police responded to a total of 96 calls Sunday, including 11 medical emergencies, two fires; 10 alarm activations, and three other arrests.
The charges included: driving while intoxicated, unlawful possession of marijuana, and vehicle and traffic violations.
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