Petit theft is a misdemeanor. It can either be a second-degree misdemeanor or a first-degree misdemeanor depending on the value of the property stolen. Under $100 is a second-degree misdemeanor, over $100 (or with a subsequent petit theft convicted) and you are facing a first-degree misdemeanor.
Most petit theft cases are instances of shoplifting. While it may be a misdemeanor, it can be considered a crime involving moral turpitude, which may have immigration consquences if you are not a U.S. citizen and you plead guilty or no contest or are found guilty.
Petit theft is typically proven when the prosecutor calls the LPO (loss prevention officer), or store security guard, as a witness. The LPO will testify that they saw the accused take the item and walk past the point of sale (cash register). Sometimes, a video can be introduced into evidence showing the theft on the store's closed-circuit TV.
In most petit theft case, the arresting officer is not a necessary witness because they didn't witness the theft. The arresting officer may only be called if the accused made a statement in the presence of that officer.
Many stores want accused shoplifters to sign statements admitting guilt. You cannot be forced to sign a statement. However, you do not have the same rights that you have when a police officer is trying to get a statement out of you. A store security guard is not a police officer, therefore they do not have the authority or the requirement to read you your Miranda rights. If you are accused of shoplifting by a store security guard, I advise that you do not sign any statements of guilt nor issue a statement, written or verbal, to anybody.
Petit theft can be tried before a judge (non-jury or bench trial) or a jury. However, the state must be ready to proceed on trial day. If the state cannot prove its case, it may be possible for your lawyer to get the charges dismissed.