Sussex Police want the Home Secretary to order a review into the James Ashley shooting and subsequent investigations.
Chief Constable Paul Whitehouse, hit with a barrage of calls for his resignation, has written to Jack Straw who is already under pressure to hold a full public inquiry.
A spokesman for Mr Whitehouse said: "We need to find out how we came to be where we are now and to see if there are lessons to be learned."
The family of Mr Ashley, who was shot dead by an officer while unarmed, has also called for an independent inquiry to be held.
There has been an outcry over the 40 months it took from the day of the shooting to the end of criminal proceedings this week.
All five officers involved were cleared of wrongdoing even before all the facts were presented to juries.
Mr Whitehouse, strongly criticised over his comments following the fatal shooting in Hastings in 1998, has asked a team of senior officers to conduct an inquiry into what went wrong.
The spokesman said: "We have never before been able to deconstruct the operation because such a large number of people were warned as witnesses and therefore we were unable to speak to them.
"Now the criminal proceedings are over we can look at the events to see what we can learn."
Sussex Police was accused of "complete corporate failure" over the ill-fated operation in an inquiry report by Kent Police.
A trial judge said those responsible for the implementation, monitoring and good practice of firearms procedures "bear a heavy burden" over the death.
However, when Jack Straw visited Brighton and Hove yesterday and was tackled about the possibility of an inquiry, he was unable to give an answer on whether he would call for one.
He refused to be drawn by questioners, saying he would not make a decision until disciplinary procedures had been completed.
He said: "There are still matters which have to be dealt with.
"As Home Secretary, I am the ultimate court as far as appeals involving serving officers are concerned. It would be improper of me to make any comment on the actions of individual officers at this stage.
"But I will listen to representations from Mr Ashley's family and all quarters before I make a decision at the appropriate time on whether or not to hold an inquiry."
Mr Straw was speaking at Downland Court, Portslade, during an election visit.
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