I'm going to suggest that's the predecessor of money orders. Way back when, the Post Office Dept. operated a savings bank and as well offered a whole lot of money transfer functions. So this was a good-as-cash certificate that the recipient would cash at the receiving post office, and the sender had his / her receipt for the $3 sent.
Postal notes were a form of money orders for small remittances. The form indicated a dollar amount and the odd cents were indicated by postal note (or postal script) stamps affixed to the postal note form. The stamps were first issued in 1932 and the last issue was in 1967.
Definitely a money order form. Some of the Canadian offices could either issue and cash money orders, but, most of the smaller offices could issue them only and could not cash them.
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