ButThe [American] rule is to place a period after each abbreviation…
Abbreviations of the following titles…are proper in any writing: Mr., Mrs., Messrs., Dr. –Walsh Handbook
However, the British use seems to have fallen to the American use.According to British usage, if the abbreviation ends with the same letter as the word entire, no period is necessary:
If the abbreviation ends with a letter other than the one that ends the whole word, a period is called for:
As is not uncommon, the common modern American use is in fact the older British use. A modern Briton who abbreviates Mister as "Mr." with the punctuation mark is in fact following the universal practice of 18th C. and early 19th C. England, Scotland, Ireland, and Wales.However, the British use seems to have fallen to the American use.