From NRA High Power rule book, rule 15 - Decision of ties.
First part of the rule (15 - a and 15 - b) talks about decisions by X, and there are rules if shooting was done at multiple distances (e.g. Palma aggregate).
In a 'regular' F-class match, at a single distance, if shooters have the same score and the same number of X, the rule says (15 - c):
(c) In the event the tie is not broken, the scores at each range, in the above order will be ranked:
(1) By the fewest misses.
(2) By the fewest hits of lowest value.
(3) By the fewest hits of next lowest value.
(4) In slow fire individual stages, by the value of the hits in inverse order, counting singly from last to first (X’s being hits of highest value).
C-1 probably does not decide a lot of ties but in really tough conditions it could.
C-2 and C-3 would mean that if two shooters tied, but one shot an 8 and another only shot 9's (for the shots that were not 10 or X that is), the shooter who shot an 8 loses.
C-4 is what I have colloquially heard referred to as 'Creedmoring'. Starting from the last shot of the match, compare the two scorecards and working backwards, when the two competitors do not have the same score for the shot, the one with the higher wins.
For example, if both shooters ended with an X for shot 20, but shooter 1 has an X for shot 19 and shooter 2 has a 10 for shot 19, shooter 1 wins. Working back like that until there is a difference.
If this still does not break the tie there is rule 15.13 - Unbreakable Ties:
15.13 Unbreakable Ties — In any case where a tie cannot be ranked under the foregoing provisions of this section, the Match Director will direct that the tie be decided and prizes awarded under one of the following plans as appears necessary or advisable:
(a) By firing of a complete or partial score under the original match conditions or at longest range of the match.
(b) By drawing of lots for merchandise, medal or trophy awards, and combining any cash awards to which those tied may be entitled and equal division of such cash among those tied.
15.13 (b) essentially being the good old coin toss