Taylor's killing came in the early-morning hours of March 13, when several officers arrived at her apartment and knocked several times.
Police said the boyfriend, Kenneth Walker, fired once at them, giving them cause to fire back, killing Taylor but not hitting Walker.
No drugs or money were found at Taylor's home the night she was killed.
Their union, the River City Fraternal Order of Police, said it was "aware that two of our members received pre-termination opportunity to respond notices today, outlining the chief's current intent to terminate their employment".
Interim LMPD Chief Yvette Gentry said detective Joshua Jaynes violated LMPD's standard operating procedure when obtaining a warrant for Taylor's address, saying in a termination letter to Jaynes that he failed to complete a Search Warrant Operations Plan form and lied in his affidavit.
Clay said the hearing is a formality "because there's no doubt in my mind that there's already been a decision reached to terminate him without regard to what he has to say at this pre-termination hearing". "I fully expect Mr. Jaynes will be terminated after the "hearing' no matter what the evidence is to the contrary".
'Jaynes did nothing wrong, ' Clay added.
Gentry also noted that neither Jaynes nor his supervisors were present at Taylor's apartment when the search warrant was executed.
Cosgrove, on the other hand, was present at the shooting.
But with no-knock warrants, officers don't have to say anything and don't have to wait.
None of the officers have been charged with Ms Taylor's death. The FBI concluded Cosgrove fired the shot that killed Taylor.
"These are extreme violations of our policies, which endangered others", Gentry wrote in the letter. Officer Brett Hankison, who was charged with wonton endangerment for shooting into a neighboring apartment, was sacked in June.
A lawyer representing Mr Jaynes told CBS that the officer had not created the plan himself and that senior colleagues were present when the warrant was signed off.
Another officer involved in the raid, Brett Hankison, was sacked in June. That's because the warrants are reserved for extraordinarily unsafe moments or if suspects are likely to destroy evidence if they are alerted to officers' presence, but critics say not always. No charges were filed in Taylor's death.
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