also heehaw, first recorded 1815 (as Hiu Haw), probably imitative of sound of donkey's bray (cf. French hinham). As "a loud laugh" from 1843.
As for hee-haw, he began quietly cropping the grass, as if he had done his part of the entertainment.
(Antistrophe) hee-haw, Remus can saw, Romulus tries to make plaster.
hee-haw never runs far, an' he never did such a thing before.
From the woods at his left came the protesting "hee-haw" of a mule.
They were not the hee-haw; in fact, viewing the host of marriages, they were for discussion; there was no bray about them.
It had never wagged its tail, or tossed its head, or said, "hee-haw!"
But on a sudden we did hear a noise—a rattling and "hee-haw!"
During the second day her burro gave a rasping bray, and a hee-haw answered from the bush.
"Do hee-haw in the House of Commons, Heavyside," says the young man with a languid air.
So she presented him with an ass out of the stable, and he had but to pull Neddy's ears to make him begin at once to hee-haw!