In the MSHSAA "Official's Manual" (available at mshsaa.org), there is on page 9 a heading titled "Procedures to Follow in Case a Game is Protested."
Essentially, if the head coach feels there has been a misapplication of a rule by contest officials, he may "file a formal, verbal complaint with the game officials who will then notify the opposing coach immediately." Note this does not allow any protest judgment calls.
Under paragraph C of this section, the protesting coach is allowed to produce the NFHS rule book for the sport in question and show game officials the appropriate rule reference and how it was misapplied (in his/her opinion). There is a maximum of 10 minutes allowed for this to take place. According to this section: "If a rule reference(s), case book play(s), or other information from MSHSAA Rule Meeting Announcement and/or MSHSAA Sport Manual is found that indicates a misapplication of a rule has occurred, the official's decision shall be corrected at that time before any further action occurs, and the game shall be resumed from the point of interruption after the correction."
Finally, here's paragraph G: "Officials that fail to allow a protest of rules application or fail to make the appropriate change when shown the rule are subject to suspension of their officiating privileges."
As if this arcane concept wasn't confusing enough, paragraph A adds to the confusion for basketball officials: "Within the guidelines of each individual sport rule code, the head coach must request a review of an official's application of a rule through the appropriate channels."
I see 5-4-2 states "The NFHS Basketball Rules Committee does not recognize protests." I suppose this means in basketball, this procedure would not apply.
Basketball is the only sport I officiate...but what about you multi-sport folks out there? Do other rules allow for a protest by the coach in the middle of a game?