The Chief Constable has been accused by the UUP of "disgracefully" undermining his officers by saying they should not be allowed to investigate Troubles cases.
In a lengthy statement, Ulster Unionist Party MLA Doug Beattie slammed Simon Byrne for suggesting that current or former officers from the PSNI or RUC lacked the independence needed to be part of the proposed Historical Investigations Unit (HIU).
The HIU was agreed in 2014, with the Government promising to table legislation to implement legacy provisions within 100 days of the New Decade, New Approach deal.
Last week Mr Byrne told the Stormont Justice Committee that, on legacy cases, "we would welcome it not being the responsibility of the PSNI".
He added that the PSNI were also taking legal advice on whether the police could be considered "practically independent" on the past.
Mr Beattie commented: "This does two things - firstly and disgracefully, it undermines those who served bravely and proudly in the RUC GC, and secondly, it undermines those who now serve in the PSNI."
He added that it was wrong to "pre-judge individuals" in the security services.
This includes the terms of reference for investigating the loyalist Glenanne gang, linked to dozens of murders in the 1970s and 1980s.
Several of the gang were also members of the police and UDR and there have long been allegations of collusion in the UVF terror gang's crimes. Mr Beattie said the terms would exclude those who had ever served in Northern Ireland "as being in some way biased".
"Yet, at the same time, we as a society do not bat an eyelid at convicted terrorists being part of the Policing Board."
He added: "Even the fact that the PSNI are using the term 'state collusion', when the Attorney General says this should not be used as a descriptor, gives you an idea as to what the outcome is likely to be at the end of this review."
The MLA said he also feared the HIU would "completely undermine" the RUC: "A force that stood between the terrorists and the terrorised with professionalism, courage and dedication."
Another concern, he said, was that dissident groups could claim the police lacked independence on the past.
Mr Beattie concluded that a decision to end the Historical Enquiries Team (HET) in 2013 should be revisited before any "ill-thought-out HIU is enacted".
Assistant Chief Constable George Clarke said dealing with the past was a "challenging and highly emotive issue".
"The legal framework in this area is complex and evolving as highlighted by a range of recent court judgments," he said.
"Northern Ireland’s courts have held, in a number of recent cases, that PSNI did not (in those cases) sufficiently demonstrate practical independence. The Chief Constable has sought, via appeal to the Supreme Court, to clarify elements of those rulings as they may impact upon contemporary policing.
“The current approach to dealing with the past is not working for those people who have been grieved or for those who have and continue to suffer. That is why we are of the view that the appropriate means to address the issues arising from legacy investigations is the implementation of the Stormont House Agreement bodies.”