Well, that would depend on the nature of the crime.
It is important to distinguish Speedy trial from Statute of LImitations. As far as speedy trial is concerned, the State Attorney has 90 days to bring you to trial in cases involving misdemeanors, whereas, the State has 175 days to bring you to trial on any felonies. Of course, the purpose of speedy trial provisions is to provide a defendant with a speedy trial when he has an real desire for a speedy trial. Now, speedy trial is only an issue post arrest.
Requesting a speedy trial is not always in the one's best interest and must be viewed on a case by case basis.
However, Statute of limitations is the law determing the amount of time from the commission of the crime that one can be charged, for instance, felony that resulted in death: none;
1st degree felony and 2nd degree felony for abuse or neglect of aged or disabled adult: 5 yrs.; others: 3 yrs typically; any offense with fraud 3 yrs.; sexual offenses (battery, assault, intercourse under age 18): begins running at age 16 or when violation is reported, whichever is earlier.
Misdemeanors Other 1st degree misdemeanors: 2 yrs.; 2nd degree and noncriminal violations: 1 yr.
Of course, the law is constantly changing, so best to check with an attorney.
The state has until the statute of limitations expires to charge you. That time limit varies depending on the crime. However, because you were arrested, the state has to either file charges or no file the case. This usually occurs about 30 days after the arrest. If the state takes no action, your speedy trial rights are running that allow for a dismissal after 160 days pass for a felony. A motion has to be filed and a 15 day window period is given to the state if that happens. It's in your best interest to contact an experienced criminal attorney in your area to review your case to determine your rights and take appropriate action.
The way you phrased the question I will make some assumptions.
1. The alleged crime occurred fairly recently, and;
2. You were arrested for that alleged crime shortly thereafter, and;
3. You are now out of jail.
If this is correct, then the statute of limitations does not apply. Your arrest signals the start of prosecution and that prosecution started shortly after the allege crime was committed.
As you are not in jail, the next time period that concerns you would be the expiration of speedy trial. This period is 90 days for misdemeanors and 175 days for felony charges. The state has to file formal charges by Information within those time periods as calculated from the day of your arrest. These time periods run whether you are locked up or not, and whether you demand speedy or not. Be aware that if misdemeanor and felony charges are joined in a single Information, speedy is 175 days for all.
If that time period passes and you have not been charged - do nothing. That should simply be the end of it. If you file notice of expiration, which would be important IF you had already been charged and want your trial, you will simply be giving the state notice that they have forgotten to file charges against you and now have only 15 days more to do so. Don't be so kind - let them do their own calendar watching.
IF for some reason the state picks up the case and files an information after speedy has run, you will get a court date for an arraignment. At that time you need an attorney to file a motion to discharge. If no one objects, and no motion is filed, your case would proceed as if there were no speedy trial rule, so it is important to be aware and to have an attorney.
Because speedy trial runs regardless of whether you are in jail or not and begins from the date of your arrest, filing charges after speedy violates your right to a speedy trial and as such entitles you to discharge, with prejudice, from all charges arising from that "criminal episode." The state then has 30 days to appeal.
By the way you phrased the question, Mr. Mosca is correct. You are now on the speedy trial time schedule which means the State has 175 days from the date of arrest to bring you to trial for a felony and 90 days for a misdemeanor charge. Unfortunately, speedy trial does not have the "punch" it use to now that the state can surpass that time and the defense is required to "notice" them of their delay.
The State must file official charges by those time frames, otherwise they will be barred (so long as your defense counsel points this out).