Despite a high vaccination rate in the town and statewide, the positive infection rate reported by the testing sites at Town Hall and in Montauk more than tripled in August, from 4 to 13 percent of those tested receiving a positive diagnosis. Between Sept. 14 and 19, the positive rate was 12.2 percent among 1,263 tests in East Hampton and 13.5 percent among 370 tests in Montauk.