I’m writing a letter to the mayor (a woman) of my city. How should she be addressed?
Dear Madame Mayor
Dear Mrs. Mayor
Dear Mrs. Hasara (her name)
Dear Mayor Hasara
Dear Karen 
Thank you.
‘Dear Mayor X’ is correct, according to
this page.
According to my copy of “The Essential Writer’s Companion” (3 book set with a desk dictionary and thesaurus):
Forms of address do not always follow set guidelines; the type of salutation is often determined by the relationship between correspondents or by the purpose and content of the letter…
In formal salutations, when the addressee is a woman, “Madam” should be subsituted for “Sir”. When the salutation is informal, "Mrs. or “Ms.” or “Miss” should be substituted for “Mr.” If a woman addressee has previously stated a preference for a particular form of address, this form should be used.
Form of Address (envelope)
The Honorable <first and last name>
Mayor of <city>
Salutation
Dear Mayor <last name>:
I believe in Canada its “Lord” or “Worship”…or something utterly ridiculous like that.
Brown paper, string and a large indelible marker.
Works for me.