Pick a card
The Iowa coin tosses that settled some disputes in the presidential caucuses and also threw the final result into question have sometimes been used in Nevada. That is, chance has been used, though not specifically coin tosses.
In 2002, a 107-107 tie in an Esmeralda county commission race was settled by choosing cards from a new deck fanned out, high card winning.
Ties in a 1982 contest for Eureka county clerk and a 1972 Gabbs justice of the peace race were also settled with cards.
Some states have used drawing lots in the case of ties.