Glad you asked...
When writing a formal letter to a judge it is important to address them with correctly. When I say address them I mean their title for instance the first line should have the word "Honorable" and their name then underneath their exact position. It's important to proofread your letter before sending. You can find more information here: http://www.freesampleletters.org/sample-...
Then again, this answer might help you...
To write a formal letter to a judge, you should always address them as such. Also, be sure to use proper grammar as they may be intolerant of ignorance.

