IF THE POLICE CALL YOU
Generally, the police won't call you. They'll just come to your door and arrest you. However, if you should receive a telephone call from the police and they start asking you questions, don't expect that you can talk your way out of a situation or explain it away. In fact, don't try. They aren't really listening. By the time the police call you or leave a card for you, they've already got their sights set on you and more than likely are just trying to locate you so a police car can be at your front door by the time you get off the phone. Instead of trying to be friendly or helpful, tell them immediately that you have a lawyer and they can speak to him/her. That usually will put an end to the call pretty quickly. However, if that happens, make sure to immediately contact a lawyer so you're covered if and when the police call again for a name of your attorney.
IF THE POLICE LEAVE A BUSINESS CARD TO CALL THEM
If you find a Detective's business card at your door with a note saying "call me", its usually best to call an attorney first. Usually, when you call a Detective, they've already settled on you being their "Perpetrator" and they're simply trying to get you to surrender. They will probably not tell you that in advance becaue they don't want to spook you, but that's usually why they leave their card. Sometimes, they're simply looking for witnesses, but you won't know that until you or your lawyer speaks with them. That's why its best to get a lawyer to call them first. A lawyer can usually discern whether they actually just want to speak with you to see if you're a witness or if they want to arrest you. Don't believe for a second that you can call them and talk them out of anything. That's not the case. Once they are looking at you, they usually want you and anytihng you say will be interpreted against you. Call a lawyer and let them speak to the police.
ANYTHING YOU SAY WILL BE INTERPRETED AGAINST YOU
While the "Miranda Rights" that all police are obligated to inform you of before questioning you apply, remember, if you speak with the police, they are going to be hearing you with "prejudiced ears." That means that anything you say that could be interpreted against you - WILL be interpreted against you. Even things that aren't open to interpretation will be considered against you by them. What you should understand here is you can't talk your way out of it if someone has already submitted a Complaint against you. Don't bother to try. All you'll be doing is digging a deeper hole for yourself.
WHEN YOU FIND A POLICE BUSINESS CARD - HIRE A LAWYER FIRST
Hire an experienced criminal defense lawyer first and have them make the phone call to the police. They will be able to determine if you are the primary suspect and if there is any room for "talking" your way out. If not, just by hiring them, you've insulated yourself from being questioned by the police. The lawyer will accompany you to the Precinct and sit with you if you're being questioned and stop the police from going any further than he/she wants to allow. This is all very important for you. So hire an experienced lawyer first.