What is the proper heading when writing a judge of a circuit court?

Answer:
Hon. (judge's name)
Judge, (Court District) ex. 17th Judicial Circuit
(State Court) ex. State of Illinois
Address
City, state, zip

Dear Judge (insert his/her last name) :


Sign the letter "Respectfully", then your signature block.

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Usually, you refer to a judge as "Your Honor", but in letters, I don't know if there's something specific. You could say "Attn: Judge %26lt;name%26gt;", if you know the name.