How should I address a female who is senior to me (in both age and rank) in an official letter?
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As an Australian English speaker working in a typical office environment (health/academic sector), if first name use is not appropriate ('Dear Janet') then I would use the person's preferred title depending on their position or qualifications:
This should be fine in most contexts irrespective of gender.
I think it would be most unusual to use 'Madam' or similar to refer to a fellow employee, no matter how senior. Perhaps if addressing the Governor General, a High Court Judge or such there may be 'protocols' that are meant to be adhered to. There are also potential cultural differences of course, with the respect accorded to high-ranking employees varying from country to country.
As Snubian said, addressing her by her title, or by Ms is appropriate and respectful.
Please don't use Madam, since that has negative connotations attached. The "mam" honorific is a shortened for of Madam, and sounds rustic and casual.
If you are writing the letter to her, write in second person. If you are writing about her to another, use third. For example.
I think Madam or Ma'am is appropriate and formal. Heck, it's how you refer to the queen after the first introduction :)
Madam also lends itself well if you append her position. "Madam Chairman[woman]", "Madam President",etc...