11:57 AM PT -- Massachusetts officials say the Medical Examiner WILL release Aaron's brain to Boston University ... but they have not given a specific time frame.

"The Office of the Chief Medical Examiner is conducting an investigation into the circumstances of Aaron Hernandez’s death, which may require further analysis of his body," the Secretary of Public Safety and Security said.

"Once that is complete the brain will be released to Boston University. No one is going to stand in the way of the family’s wishes for Boston University to have Aaron Hernandez’s brain."

There's a standoff over Aaron Hernandez's brain.

Hernandez's lawyer, Jose Baez, just accused the Worcester Medical Examiner of illegally retaining Aaron's brain after agreeing to release it to the hospital of the family's choice for the purpose of CTE medical research.

Baez says the M.E. actually agreed to send the brain to Boston University CTE unit, which is renowned in the field. The family wants to know if Aaron was affected by CTE and hopes the examination will help other families.

Baez says a doctor in the Medical Examiner's Office went back on the deal and decided they would keep the brain and do the exam, rather than sending it to B.U.

The attorney is threatening a lawsuit if the M.E. continues to withhold the brain.

What's particularly interesting ... Aaron Hernandez's brain is irrelevant to his time in prison, the murder of which he was convicted or anything else involving the justice system.

The brain has everything to do with football -- something in which the prison has no involvement.

Since the prison says he committed suicide, there's nothing revealing about examining his brain.