Rashi states, זאת חקת התורה: לפי שהשטן ואומות העולם מונין את ישראל לומר מה המצוה הזאת ומה טעם יש בה, לפיכך כתב בה חקה, גזירה היא מלפני ואין לך רשות להרהר אחריה- This is the statute of the Torah: Because the Satan and the nations of the world will taunt the Jews and ask the Jews about their commandments and subsequent purposes. Therefore, the Torah uses the term decree. I have decreed it; you have no right to challenge it.
This answer seems to imply that there is no reason for this commandment of Parah Admuah; we simply keep it out of blind faith. Rashi 19:22 states in the name of Rabbi Moshe HaDarshan that it atones for the sin of eigel (the golden calf). We are left with a question; is it a chok or to atone for eigel?
The Bikurei Avraham and Kehilas Yitzchak answer that all the different explanations for Parah Adumah (the red heifer) conclude that it atones for eigel, precisely because Parah Adumah has no reason. The sin of eigel was that the Jews threw off the yoke of heaven, so the equal and opposite would be to accept the yoke of heaven despite not knowing the reason. Thus, both answers ring true - we don’t know the reason for Parah Adumah, and that’s why it atones for eigel.