At the drop of a hat

I am sorry the jacket cannot be traced," Chidambaram said. He also reacted angrily to Mumbai cops' tendency to rush to the media at the drop of a hat. "Mumbai Police cannot speak to media out of turn. Their job is to enforce law and order," he said.
source : http://www.dnaindia.com/bangalore/report_chidambaram-slams-mumbai-cops-for-losing-their-focus_1316610

Please explain to me the emboldened parts.