The investigation, code-named Operation Russell, allegedly raised questions about former commander Ray Adams's conduct before the Lawrence case, the Guardian said.
There was reportedly insufficient evidence to bring criminal charges and Adams told the newspaper this exonerates him and denied any wrongdoing.
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Police say they have traced four drivers who are thought to have hit the woman, and added that a fifth vehicle may also have been involved.
Alex Rowley said he was "disappointed" that Scottish Labour Party were unable to fully investigate harassment claims against him.
Widespread frost, fog and icy stretches overnight. Rain for most during tomorrow