The Mishna says that if one has a safeik whether they have a peter chamor, they must redeem it with a sheep but don't need to give it to the kohein since the rule for giving is המוציא מחבירו עליו הראיה - the burden of proof is on the collector. The gemara says that this follows the opinion of R. Yehuda who says that a peter chamor is forbidden to derive benefit from, therefore one must redeem it even though it won't be given, but according to R. Shimon who says that it is permitted, there isn't even a mitzvah to redeem it.
Tosafos raises an interesting question - A peter chamor without redemption requires it's neck to be broken. Since the mitzvah to break it's neck (arifa) is like any mitzvah where we are strict when there is a doubt, even if it weren't assur b'hanah, there should be a requirement to break it's neck. Tosafos answer cryptically and says that just as one doesn't need to give it to the kohein, there is also no requirement to do the arifa out of safeik. It isn't clear what Tosafos means to say - the concept of המוציא מחבירו עליו הראיה exempts the giving to the kohein but doesn't exempt the breaking of it's neck?
The Maharit Algazi suggests that since we have a concept of המוציא מחבירו עליו הראיה and apply it even to mitzvos that one is obligated to do by the torah such as all safeik of gifts to the kohein, we can similarly apply this concept to any mitzvah where it is questionable if one needs to fulfill it and the fulfilling of it would entail a loss of money. Since the arifa of the peter chamor would be a loss of money, one isn't required to incur the loss for a safeik mitzvah.
This approach is very difficult to accept. It should follow that if one is in doubt whether they are obligated in matzah on pesach or whether they have already fulfilled their mitzvah, they shouldn't be required to incur any expense to fulfill the mitzvah. Had this been true, it should have been mentioned in earlier poskim. Rather, we generally assume that this rule is limited to mitzvos that require giving, but doesn't apply to expenses that need to be incurred to fulfill mitzvos between man and G-d. Therefore, this concept shouldn't apply to the mitzvah of arifa (breaking the donkeys neck).
The Rashash explains that Tosafos doesn't mean to fully equate the mitzvah of breaking the neck with the giving to the kohein, since the concept of המוציא מחבירו עליו הראיה wouldn't apply to the mitzvah of arifa. Rather, Tosafos holds that the arifa is the consequence when one doesn't fulfill the mitzvah to give the sheep to the kohein as redemption of the newborn donkey which is incumbent upon him. When there is no requirement to give a sheep to the kohein, the mitzvah of arifa would also not apply.