If your neighbor does not remove the dangerous tree, and the tree does in fact cause damage, your neighbor can be held liable. If you have spoken to your neighbor about the tree issue, and he has not done anything about it you do have laws that protect you.
Felonies are the most serious type of criminal offense. Felonies often involve serious physical harm (or threat of harm) to victims, but they also include offenses like white collar crimes and fraud schemes. Offenses that otherwise are misdemeanors can be elevated to felonies for second-time offenders.
If you were charged with theft in the third degree (sometimes referred to as Theft III) or theft in the second degree (Theft II), you are charged with a misdemeanor crime. If you were charged with theft in the first degree (Theft I) or aggravated theft in the first degree, then you are facing a felony charge. There are other related charges such as identity theft; forgery; criminal possession of a forged instrument; etc. which are outside the scope of the discussion here.