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If you're writing a full address in the middle of a sentence, complete with zip code, this is the correct format:
Ex: Our address is 12 Brook Lane, Apt. 3, Kansas City, MO 64011.
If you are not providing the zip code, this is the format:
Ex: Our address is 12 Brook Lane, Apt. 3, Kansas City, Missouri.
(If you want to abbreviate the state, it has to be the old formal abbreviation, which in this case would be "Mo.")
There is an exception to the rule on an address that is completed with the ZIP Code: When used on an envelope or cited as for use on an envelope, there should be no comma between the city and state or territory. In the first use of the ZIP Code system in 1963 (and since) the state, etc. was to be capitalized and without punctuation, thus ensuring readability by the OCR software that was and is used. I will admit, that as a 36+ year of the USPS, I observed wholesale ignorance of this by management and co-workers.