No I cannot think of a case offhand where LE admitted they lied during the course of an investigation, that is not the kind of thing LE broadcasts. But I would venture to say they twist the truth to suit their own purposes in every investigation that LE has ever done and will ever do. In HB case for example, maybe the perp has no idea CB caught a glimpse of him and LE shared that info to rattle his cage. Maybe CB didn't see anything, either way it would worry a perp to think they were spotted when they were not aware of it. These kinds of lies, not the sky is purple and pink when we know it is blue type of lies. On the flipside, if LE takes this to far then rumors begin to swirl around falsehoods and really muddies the waters. That is my concern for what would happen in this case and is still a HUGE concern. LE even admitted the rumors were to much to process.
I know this is not what you were getting at, but here is one case I found where the LE was caught lying during trial testimony in a drug case. This is farrrrr worse that what you were asking for, IMO, because this happened during a trial. Many other stories just like this as well.
An Exclusionary Rule for Police Lies
In July, 2008, two officers of the Los Angeles Police Department took an oath in
a criminal jury trial and testified that the defendant, who was charged with possessing
cocaine, had run from them before throwing a black box, which concealed both powder
and crack cocaine.
Normally, the officers testimony would have been sufficient to
convict the defendant. But this time the officers testimony fell short. Unknown to the
police, the whole incident had been captured on a grainy video from a surveillance
camera mounted on a nearby apartment building.
The video, which the defendants lawyer produced for the first time at trial, sharply contradicted the testimony of the two police officers.
As a result of the tape, the prosecutor moved to dismiss the case, and
the judge agreed.
http://works.bepress.com/cgi/viewco...&sei-redir=1#search="cases where police lied"
And here is what you were getting at!
Jerome H. Skolnick, author of Justice without Trial: Law Enforcement in a Democratic Society, is Professor of Law and Director of the Center for the Study of Law and Society at the University of California, Berkeley.
(1997 note: Professor Skolnick is currently Adjunct Professor of Law at New York University Law School, and Co-Director of the Center for Research in Crime and Justice.)
Deception by police- Jerome H. Skolnick
Whatever the answer to that question--if, indeed, an answer be formulated--it has to be measured against a hard reality of the criminal justice system. That reality is: Deception is considered by police--and courts as well--to be as natural to detecting as pouncing is to a cat. As we shall see, that is why it is so difficult both to control deceptive practices of detectives and to prescribe long-term measures to guarantee control.
The Stages of Detecting
Deception occurs at three stages of the detecting process: investigation, interrogation, and testimony. If we place these three stages within the framework of a broad portrait of the moral cognition of the policeman, we observe that the acceptability of deception varies inversely with the level of the criminal process. Thus, deception is most acceptable to police-- as it is to the courts -- at the investigation stage, less acceptable during interrogation, and least acceptable in the courtroom.
http://www.lib.jjay.cuny.edu/cje/html/sample1.html