Boone County, KY in 1976 (Carter and Ford 5,602 votes (49.21%) apiece, seven others 181 votes (1.59%) between them), and next-door
Gallatin County, KY in 1984 (Reagan and Mondale 1,042 votes (49.78%) apiece, four others 9 votes (0.43%) between them).
Also, check out the Republican non-Presidential primaries under this Atlas's
Kentucky Election Results home page, when tied counties were a fairly regular occurance into the 90s it seems as the total number of votes cast was very low in some counties.
