Tie votes in STAR Voting are rare -well over 10 times less often than with choose-one voting- but as with any voting method they can occur, especially in elections without many voters.
In most cases, ties in STAR voting can be broken by referring back to the ballots themselves. Ties in the Scoring round should be broken in favor of the candidate who was preferred by more voters. Ties in the Runoff round should be broken in favor of the candidate who was scored higher. Ties which can not be broken as above are considered a true tie.
True ties can be broken by random selection, as outlined in the bylaws or charter governing the election in question. Alternately, if complexity is not an issue they can be broken using another voting method such as Minimax voting.