Reading them their Rights

Your Rights:
“You have the right to remain silent. If you give up that right, anything you say may be used against you in a court of law. You have the right to consult with an attorney and to have one present during questioning. If you can not afford an attorney, one will be provided for you. If you choose to talk to a police officer, you have the right to stop the interview at any time. Do you understand these rights as I have read them to you?”

What you can and can't do:
In real life there's a lot of rules and regulations about what cops can and can't do in their work.

However this is a game and so I'll just mention a couple of rules that commonly show up in police stories.

Use of Force
Basically Cops should use reasonable force to aprehend suspects. Shooting an unarmed pick-pocket is murder and police officers can still be tried for that.

Officers who manage to talk a criminal down or use absolute minimum force often have an excellent reputation (gaining the Network and/or Status Merits) and are sure bets for promotion. Conversely people who regularly use extreme force (even if it is technically within guidelines) may be marginalized by most cops and passed over for promotion.

In practical terms you should use force one stage more serious than the force used against you on the chart below. So you may restrain somebody physically if they are being verbally abusive to you but beating them with your baton would be excessive force. Likewise it would be excessive to shoot somebody who was trying to punch you in order to escape, but if that person had a knife then using a gun would be justified. This assumes that the officers’ life is not in serious danger, simply trying to arrest a suspect. If your life or another persons life is in serious danger, take them down and use whatever means it takes as long as you avoid civilian casualties. If somebody is foaming at the mouth and throwing people around like rag-dolls, you're probably okay to use lethal force.
 * Loud verbal commands/threats (Officers should not be abusive)
 * “ Soft hand” Compliance holds such as arm locks or physically restraining a person (In game terms grappling or handcuffing)
 * Non-lethal force: (common sense applies here, don’t kill/maim them)
 * Chemical irritants: CS/tear gas or pepper spray
 * Authorised Electrical weapons: Ranged stun guns or tasers
 * Authorised impact weapons: Batons, Sap gloves, rubber bullets
 * Hard Brawling: Any punches, kicks and martial arts manoeuvres.
 * Lethal force: Any authorised firearms. In desperation do anything to survive
 * Any suspicious deaths of suspects will be investigated. So be careful.

Searching and arresting

 * You do not have to arrest everybody for every crime, most minor offences (Possession of drugs, prostitution, drunk and disorderly) are dealt with without an arrest (confiscating drugs/booze, getting a cab for the drunk, giving the girl a help-line number and getting her to go home with a verbal warning) Sometimes regular misdemeanour criminals can even become helpful informants if you treat them fairly. Stopping the criminal activity is important and sometimes arrests are needed, use your best judgement.
 * However there is no leeway in felonies or when the victim presses charges, in these cases you must arrest them (even if they are a family member or another cop).
 * Arresting a person requires:
 * Probable cause (Reasonable evidence the person is the criminal, you don’t have to be 100% certain, as long as there is some evidence that the suspect committed the crime like a witness, or blood on clothes)
 * An arrest warrant may be issued by a judge against a person, if later evidence shows a link between the suspect and a crime, ask dispatch if you need any advice.
 * If you arrest anybody you must immediately read the rights to the suspect (see the Miranda rights above). Failure to do so can result in them going free or evidence being inadmissible. If you want to read the rights above, that would be cool, if you want to just say "I read them their rights" that's also fine.