Was it ever explicitly stated? My top three guesses would be Arkansas, Tennessee, or Kentucky.
I always thought it was Arkansas. I did a quick search to verify and all I find are references to them being from the Ozarks. While the Ozarks does fit with Arkansas, it would also include the southern part of Missouri. However, Tennessee and Kentucky would be ruled out.
I don’t believe it was ever stated.
Whilst Googling, I found this site and this quote:
I think they were from the state of denial? 
They’re from Springfield, of course!
In one episode, Granny said she was born in Tennessee. Doesn’t answer where Uncle Jed lived, though.
Granny was from Tennessee. The rest were from Bugtussle, Missouri.
The oil was said to have been the “Texas T”, possibly giving some insight into the location of said oil.
Granny was from Bugtussle, just find what state that is in.
Let’s see now…there’s a little panhandle in southeast Mo. that sits in between Tennessee, Kentucky and Arkansas. It’s the place that Josey Wales came through and met Granny at the ferry. Remember he sent ‘em on a Missoura’ boat ride. Notice all the little towns in the area lots of 'em end w/ …ville like Hornyville, Leachville, Portageville, Piggville, Hooterville, Bugtussle, and Evening Shade is right down the road.
Yep folks if’n ya wanna get away from the rat race, that’s the place. 
jnglmassiv writes:
> “Texas T”
It’s Texas tea.
Oil put the “T” in Texas. Before the oil rush, what was Texas good for?
Granted you could still ask that today 
No, only giving insight into the predominance of oil in Texas.
That was my take also. Sort of a"Without oil, could there be a Texas?" type-a-thing. However, reading various song lyric websites, I see that the ‘tea’ version does appear correct. I stand corrected…Thanks again, SDMB!!
So without oil Texas is basically a useless patch of desert filled w/ rednecks? Forget about the cattle industry and agriculture. Its coastal ports and railroad connections. No history or culture despite European presence since BEFORE Jamestown. No contributions to the Nation, pretty much a state full of users and losers. Except for that oil thing, right. Does that about sum it up? Nice 
Jimmy Rogers had a song once, T for Texas…just a little wordplay, oil is “Texas Tea”
It was just an afterthought.
There is a Bug Tussle Oklahoma. Although that fits nicely with the oil theme, I’ve never thought of the Clampett’s as from Oklahoma. Mr. Brewster was from Tulsa.
BTW: thought I’d mention what made me think to ask:
I was watching the DVD of Attack of the Clones with my wife this weekend. At the scene where Jar-Jar, standing in for the absent Senator Amidala, introduces the measure to grant Supreme Chancellor Palpatine emergency powers of decree, I commented that “This is like having Jethro Bodine as the senator (Rep.) from ____” ; and then I realized I didn’t know what state to give this “honor” to.
I remember someone was telling Granny about evolution and how people descended from fishs. Granny responded by saying “the only sea I’m from is Tennessee.”
Just FYI, that part of Missouri is called the “bootheel”.
I know the movie isn’t canon, but the Clampetts do comment about "Cousin Bill’ (Clinton), so make of that what you will.