Passive participation - the dummy must play cards only when explicitly directed and named by the declarer.  The dummy must never touch or play a card on their own initiative (even if it's a singleton or there are cards of equal value).

THE RIGHTS OF THE DUMMY

The dummy has the right to ask the declarer (their partner) if they have a card of the suit led when declarer fails to follow suit.  The dummy has the right to stop declarer from playing from the wrong hand.

Laws 42 and 43 of the Laws of Duplicate Bridge cover the role and rights of dummy.

Your attention is drawn to Laws 12,16 and 73 relating to hesitations.  Also Law 66 relating to arrangement of tricks.

HESITATIONS 

By far the most common form of unauthorised information is the pause that suggests doubt, generally called a hesitation.  It is important to understand that thinking about the hand IS hesitating.  

In deciding whether a "hesitation" points to a particular course of action by Partner, the Director may be helped by the following rule of thumb.

1.If a player hesitates and then passes he would welcome a bid or double from  partner.

2. If a player hesitates and then doubles, he would be unhappy if his partner removed the double.

3. After a suit is agreed if a player hesitates and then bids no trumps , he would not be unhappy to hear his partner go back to the agreed sui

ARRANGEMENT OF TRICKS

EXAMINING THE LAST CARD PLAYED (LAW 66)

Until a lead is made to the following trick, Declarer or either Defender may re-examine his own card played, taking care not to expose it to any other player.  A player who has not yet turned over his card may require all cards just played to the trick to be refaced.

HESITATIONS AND UNAUTHORISED INFORMATION

"Authorised information" on which players are entitled to base their own Calls and Plays can be imparted between partners only through Calls, (bids, passes doubles and redoubles) and plays   Information which a player receives which is not "Authorised" as above may not be put too use.  Examples of actions which may convey "Unauthorised Information" during an Auction are:

A remark or question by partner.  Partner's answer to the question.  Special emphasis or tone of voice.  A gesture, movement or mannerism.  An unmistakeable hesitation (or undue haste) before calling.