"We have registered a case under sections 507 (criminal intimidation by an anonymous communication) and 509 (word, gesture or act intended to insult the modesty of a woman) against an unknown person," Deputy Commissioner of Police Prathap Dighavkar said.
The anonymous person called Pooja last night, police sources said.
The 40-year old filmmaker approached the Bandra police station in suburban Mumbai today, following which police registered a case.
Police would go through the CDR (call data record) and try to identify the anonymous caller, they said.
Earlier, the actress-filmmaker posted on micro-blogging website Twitter about the incident.
"Off to Bandra police station to file an official complaint with regards to receiving abusive/threatening calls... Last night. Have been getting threatening, obscene calls. The male voice, obviously inebriated abused me & threatened to come over," she tweeted.