Rye New York

The township of Rye, New York State, USA, was founded early in the 17th century by settlers from Rye, Sussex.
Both parishes observe the second Sunday in Advent as an annual day of commemoration. The Rectors of both churches exchange greetings which are read out at the main service in each church.  (2011 greetings from Christ's Church here and to Christ's Church here)
An inscribed slab under the tower crossing was donated by the Americans, and in return a piece of stone from the fabric of St Mary's was sent to Christ's Church, Rye, New York.

Their website is www.ccrye.org.