Versova police here recorded Verma's statement for nearly three hours, a police officer said.
Joshi had earlier alleged that Sharma molested her when she visited his clinic in suburban Khar.
Senior inspector of Versova police station Ravindra Pawar refused to reveal what Sharma told the police.
However, another officer said on the condition of anonymity said that police were probing all the angles, including the possibility of foul play.
Apart from Dr Sharma, police have recorded the statements of seven witnesses including Shikha's room-mate Madhu who recorded Shikha's statement on her cellphone while the actress lay bleeding after slashing her own neck.
Shikha Joshi (40), who had appeared in the 2013 film 'BA Pass', allegedly committed suicide by slitting her throat at a MHADA colony flat in suburban Versova on Saturday evening.