The pertinent rule is: 15. Decision of ties
Match winner in rifle is GENERALLY decided by shootoffs on turkeys. ALL shooters (no matter what class), when competing for overall winner, shootoff on the same animal.
CLASS winners shootoff on their respective animals.
The reason for the 'generally' remark is that 15.3(b) specifically says that "Alternate methods of tie breaking may be used." (But those alternatives are NOT defined.)
IOW, while the norm is for everyone in contention for MW to shoot 'one-shot sudden death' on turkeys, you may also (AFAIK) shoot five shot strings, use reverse animal count, flip a coin, base it on who's tallest/shortest/cutest, have their wives/husbands/girlfriends/boyfriends mud-wrestle for it...or do just about anything else you want! :-D
This assumes that we're talking about SB or HP.
BPCR is a little different.