Can the home team remove the official book from the table at halftime to take to the locker room? Is it referenced somewhere in the rule book, or does this follow under the "referee shall rule on anything not covered in the rules."

It is a Tec to the coach of the team who removes the book at halftime and takes it to the locker room...this is addressed somewhere, I just don't know the exact case play/rule.

2-11-11
The official scorebook shall remain at the scorers' table throughout the game, including all intermissions.

However, there is nothing that states that it is a T to take the book from the table.

I would issue the T based on the "unsportsmanlike conduct" rule. The coach knows, or should know, that the official book staysat the table until the final horn and the officials have left the visual confines of the court.

I do not see this as unsportsmanlike. This is listed under
scorer's duties, therefore I take it to mean that it is the up to the scorer to keep the book there. In other words, when the coach asked for the book, the scorer should have simply said that it was against the rules for him to take it. Did the coach forcibly wrestle it away from the scorer?
If not, I don't see giving a T. If this comes up, just inform the scorer of the rule so he will know next time.

How do you know that the coach asked that the book be brought to the locker room? Scorers are sometimes HS kids, who can do all sorts of silly things. There's normally no way we can know whether the coach asked that the book be brought to the locker room.

NCAA A.R. 21.
At half-time, the official scorer, who is a member of the home-team faculty, removed the scorebook from the scorers' table: (a) of his or her own volition; or (b) at the request of the home team coach. RULING: In (a), when the removal is inadvertent and momentary, there should be no penalty. When there is evidence that the official scorer removed the scorebook to take it to the home-team dressing room, an indirect technical foul shall be assessed to the home team. In (b), when the home-team coach requests the official scorer to remove the scorebook, the home team shall be assessed a direct technical foul.

That's fine for NCAA but I've never read any such interpretation for HFHS.

Most score keepers don't know what their duties are beyond keeping score. If a head coach or any coach, for that matter, ask them for the book, they will give it to them. I would say that a T would be warranted if the head coach or an assistant took it to the locker room.

Has anyone thought that this may be one of the reasons that we delay going to the dressing room at halftime until both teams have left the gym?

If the "official book" leaves the table and goes to the home team locker room, the referee always has the right to designate the visitor's book to be the official book for the remainder of the game provided it was at the table during the first half and stayed there during half time.

A coach should know that he cannot send a player who has been replaced back into the game until after the clock has been started properly following his replacement. But when he tries to do it, you don't give him a T, you just don't let the substitute enter. I feel sure that there are coaches that don't know this rule about the book.

I had an official book end up in the locker room... We did not issue a T but what we did was had the visitor book do a cursory check, and then told the coach that any discrepancy would be resolved by going to the visitor book... ( The book went to locker room after we left and we were notifed when we got back)