Stop play, the offense has the ball, they are not moving towards the hoop, and the injured player is arguably in danger of being harmed further if you allow play to continue.
The only time you don't stop play immediately is if the offense is driving to the lane or taking a shot.

+1

If the defending coach doesn't like it, inquire if he would rather that you charge his player with a foul. He'll become quiet.

You'll always find a couple of people who get it wrong. :)

This was presented at my local board's meeting last season. If it's helpful, great. If not, I guess you can just ignore it. :)


DEALING WITH INJURIES DURING PLAY

A. Non-serious injuries

1. Examples: Twisted ankle, cramp, etc.
2. STAY WITH PLAYER!
3. If injured player’s team has the ball, or if injury occurs during a dead ball, blow whistle immediately.
4. If opponent has the ball, let them attack the basket.
5. As soon as they STOP attacking the basket, blow the whistle. Do this when:
-- the dribbler pulls up without an immediate pass or try.
-- the ball is passed AWAY from the basket.
-- a try is released.
6. When play is stopped, check the injured player.
-- If player says s/he is ok, player stays in the game and the game continues immediately.
-- If player need to be attended, start the replacement procedure (see below).

B. Serious injuries

1. Examples: Head hitting floor, knee injury, player on ground under basket.
2. STOP PLAY IMMEDIATELY!! Don’t wait. Player safety is our #1 priority.
3. Allow player to be attended on the court.
4. Once player has been removed from the court and the coach is back at the bench, then begin the replacement procedure.

C. In either case (serious or non-serious injury), if you beckon the coach or trainer – or if the coach or trainer comes on the floor without being beckoned – we MUST use the replacement procedure.

D. Replacement Procedure

1. Inform injured player’s coach that the player must be replaced OR the coach may request time-out and the player may remain in the game as long as s/he is ready to play at the end of the time-out.
2. Very important: the INJURED PLAYER’S TEAM must request the time-out in order for that player to remain in the game.
3. The team may use a 60-second or a 30-second time-out, as long as the player is ready to play at the end of the time-out.
4. If coach chooses to replace the injured player instead of using a time-out, instruct the timer to begin the 20-second replacement period, and sound a warning horn with 15 seconds remaining.
5. Allow the substitute and any other substitutes who properly reported into the game.

E. Resume play at the Point of Interruption.

1. If there was team control when you stopped play, then that team gets a throw-in at a designated spot closest to where the ball was. The shot clock is not reset.
2. If a try had been released when you stopped play, then there was no team control. So:
-- if the try was successful, resume with a throw-in anywhere along the endline for the team that did not score the basket.
-- if the try was not successful, resume with an alternating possession throw-in for the team that has the arrow. Reset the shot clock, even if the offense retains possession.
3. If a basket had been scored immediately prior to the injury, resume with a throw-in anywhere along the endline for the team that did not score the basket.
4. If you stopped play when free throws were going to be attempted, then resume with the free throws.
-- If the injured player was supposed to shoot the free throws, then the injured player’s substitute shoots the free throws.
-- Remember that the injured player’s coach chooses the substitute to attempt the free throws.

F. REMEMBER: you can stop play any time you believe there is a serious injury. Don’t allow a player to hold his knee in agony because you are worried about stopping a fast break. If you judge that it may be serious, stop play immediately.

That's very helpful. Thanks, Scrapper!

Agreed. I think the part that made me think twice about it was that the guys that I disagreed with were veterans that I respected and generally agreed with. But, as you pointed out, you'll always find people who will disagree with you, be it rookie or veterans. Discussing, disagreeing, and looking up the right way to handle something is how we learn from things like this, so it's all good.

B foul or A injury.

K.I.S.S.