Fifty-six people died and more than 250 others were injured at the Valley Parade stadium in May of 1985.
A recent book by author Martin Fletcher suggested several fires had started at businesses which were owned by the club's then chairman.
The IPCC said it had not yet decided if it would be investigating.
Mr Fletcher, who was at the game and lost several family members, claims the stadium fire was one of at least nine at companies owned or associated with Stafford Heginbotham.
The Popplewell inquiry, held three weeks after the disaster, ruled that the fire was started by a spectator dropping a cigarette or a lighted match which ignited rubbish that had accumulated under an old timber stand.
The IPCC said the police referral was in relation to the force's actions during the disaster itself and the investigations that followed.
Since the publication of Mr Fletcher's book, West Yorkshire Police said it had identified what material was still available from its original enquiries and discovered "a lot of material" had been retained.
The force said it understood its decision would bring back "painful memories" for people who were at the fire or who had lost loved ones, but it was "important the concerns raised by Mr Fletcher are addressed".
Mr Fletcher, who was 12 at the time of the blaze, escaped from the stand at Valley Parade, but his father, uncle, grandfather and younger brother were killed.
Naz Shah, Labour MP for Bradford West, welcomed the police decision and said it showed they were willing to be "open and transparent".
"It is only right that unanswered questions about the original investigation and process, which was conducted in great haste, are properly addressed, the victims deserve nothing less," she said.
West Yorkshire Police has referred itself to the Independent Police Complaints Commission (IPCC) over the 1985 Bradford City fire disaster.