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The only thing you should tell this officer is that you have nothing to say to him until you have been able to speak to a lawyer. Say anything else, and you'll have confessed to a criminal offense and it will be used against you to charge you and perhaps to convict you. It will also tie your lawyer's hands when it comes to negotiating a plea or trying the case if you can't get a decent plea offer.
Anything you say to anyone other than your lawyer about this has the potential to hurt you. Being drunk is something that can be used in mitigation, but it's not going to be good enough to make this whole thing go away.
Just tell the police you don't wish to answer any questions and that you'll have your lawyer contact them once you get one.
You should not talk to the police whether he tells you that you're charged with anything or not.
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Maybe the police already have what they need to arrest you and maybe they don't. If they don't have what they need to arrest you already, then the reason that they are trying to talk to you is to get you to give them the information they need to arrest you. Police are allowed to use trickery and deceptive and coercive means to get to the bottom of a crime. If you talk to them and tell them what happened, you will wind up charged with a crime.
If they DO already have enough evidence to arrest you, then the information that you give them will help the state to convict you. There is NO up side to talking to the police under your set of circumstances.
You have a Constitutional right to remain silent and not give evidence against yourself to the other side. As soon as you do, you hurt your case. The only way you should talk to them about this incident is with a lawyer, assuming a lawyer thinks you can help yourself at all by talking.
So what you ought to do is to call the police and leave a message breaking the appointment and tell them that you will contact them again after you've reached your attorney.