Who wouldn't want their loved ones close enough to haunt their house?
You and I may think it slightly humourous or totally weird to bury someone on our property. That's because when it comes to burial, we've just picked up too many traditions over the years, and even "country folk" are a little too "city" to think about disposing of a corpse on their land.
As far as the state goes, you could go ahead and chunk your loved one in the dirt...but first, you have to check with your local country government. I would guess the more urbane the area you are checking into the less likely you're going to get an "all-clear".
Of course, family cemeteries used to be a much bigger thing. You would think that there would be more concerns about polluting groundwater, but I guess with everything else that seeps down to that level, your relative may not be that big of a deal.
There are more rules and regulations, and for some light reading, I suggest "Facts About Funerals" by the Texas Funeral Service Commission. It's full of fascinating facts like you should probably call an official before you bury someone.
So the answer is, "yes", you can bury your grandma in your backyard if it's the right backyard, and go through the correct channels. I will mention that I believe that's exactly how you get ghosts, when your dead mee-maw teams up with other spirits to haunt you because you didn't spring for a plot somewhere.