On one occasion, Post's attorneys say it took four different medical technicians 17 needle sticks to draw blood from him due to difficulty locating a vein.
They also believe that the gurney table "will most likely not hold Mr. Post's 486 lb. frame" since most operating room tables are not designed to be used with weight over 350 pounds.
Dan Tierney, a spokesman for Ohio Attorney General Mike DeWine's office, told ABCNews.com that the office could only say, "We have received the filing and we are reviewing it to determine further action."
He could not comment on when or how a decision would be made.
Issues related to the weight of inmates have arisen in the past.
In 2008, an Ohio federal court rejected death row inmate Richard Cooey's claim that he was too obese to die by injection, according to the Associated Press. The 267 pound convicted killer was executed in Oct. 2008.
It took Ohio executioners about two hours to insert IVs into the veins of Christopher Newton in 2007, according to the AP. He weighed 265 pounds and a prison spokeswoman said, at the time, that his size was part of the problem.