If you made a mistake on the date, correct it with the police or the DA.
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Making a mistake on date or time is not really a terrible thing. Many witnesses are distressed and confused. It could become a more problematic thing if you don't correct your error with the police or even the District Attorney as soon as possible. The wrong date can certainly mess up an investigation.
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All things considered, you had best correct the falsehood you stated. You no doubt signed a penal law affirmation which makes false statement liable as a misdemeanor. It is unclear if you simply put in a "wrong" date or if you used the word "yesterday" or something that is less likely to be regarded as a typo. The prosecutor (if not the police) mahy consider this as compromising the case sufficiently as to decide not to prosecute. However, if they prosecute and the defendant has an alibi for that date, for example, then you are guaranteed to get into serious trouble.
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If you got the date wrong on the supporting deposition you should call the prosecutor and explain it to her. If you lied for some reason you could be charged with making a false complaint so you would need to retain an attorney to explain it to the prosecutor. If you made up the story to get even with someone you could get a year in jail and you should also retain an attorney. You would not get in trouble for a minor error such as the exact date, but how could you say "yesterday" when it was three days earlier? That does not sound like a "mistake," it sounds like a miscommunication due to a language problem or an error in your ability to communicate properly, but people certainly know the difference between yesterday and three days ago. Please choose "best answer" if this helped you.