Gov. Jan Brewer, who disputed accounts of the execution from news media representatives, said a review would be done by Charles Ryan, head of the Department of Corrections. Stephanie Grisham, a spokeswoman for the Attorney General's Office and a witness to the execution, said "there was no gasping or snoring."
Dale Baich, a lawyer for Woods, told the Washington Post he watched his client "gasp and breathe heavily." Woods was not pronounced dead until two hours after the execution began.
The execution was conducted Wednesday afternoon at the state prison in Florida. A federal judge later that afternoon ordered the state to preserve medical evidence from Woods' body.
"There is far too much that we don't know at this point, including information about the drugs, why Arizona selected these drugs and amounts, the qualifications of the execution team, and more," Baich said in a statement. "It is important for the people of Arizona to get answers, and only an independent investigation can provide the transparency needed following an execution cloaked in secrecy that went wrong."
During Woods' final days, his lawyers won a stay on the grounds that he had a right to know the identity of the supplier of the execution drugs. But that stay was overturned.
State officials and the family of Woods' victims said that even though the execution took far longer than normal he appeared to be unconscious for most of the two hours. Others gave a different account.
Troy Hayden of KSAZ-TV, the Fox station in Phoenix, said the execution was "very disturbing to watch ... like a fish on shore gulping for air."
"At a certain point, you wondered whether he was ever going to die," Hayden said.
Woods was sentenced to death for killing his girlfriend, Debra Dietz, and her father, Eugene, in 1989. He stalked Debra after she moved out of his apartment and shot her and her father at Eugene's auto body shop in Tucson.
"Everybody here said it was excruciating," Jeanne Brown told the Arizona Republic. "You don't know what excruciating is. Seeing your dad lying there in a pool of blood, seeing your sister lying there in a pool of blood, that's excruciating."