As a permanent resident, you can only vote in local and state elections that do not require you to be a U.S. citizen. It is very important that you do not vote in national, state or local elections that require a voter to be a U.S. citizen when you are not a U.S. citizen.
If you register or vote in an election for which you do not meet the citizenship requirements, you can face criminal penalties which may include a fine and or imprisonment, and possibly deportation.
DO NOT register to vote before finalizing your naturalization. Even if your Oath ceremony is taking place in the very near future, you cannot legally tick the "Yes" box to the question "Are you a U.S. citizen," until after you officially become a citizen.
Remember: Registering or voting in an election limited to U.S. citizens when you have not yet become a U.S. citizen, or claiming to be a U.S. citizen when you are not, whether or not your intention was good and you performed the act knowingly or unknowingly, will result in serious legal consequences.

