Trial By Written Declaration...those exact words are a common way to dispute traffic tickets in California. You pay a "bail" essentially the amount of the fine and hope your compelling statement causes the ticket to be dismissed (and your money refunded). Some other jurisdictions have similar "appeal by mail" type things, though many DO NOT.
State Violations in main appear to have to be contested in person.
http://www.courts.state.me.us/maine_courts/specialized/traffic/howdoi/index.shtml