Denying the allegations, Karthik said, "My father is a respectable man. Why should I spoil it?"
A case of rape, breach of trust and cheating was registered against Karthik in Bangalore on the complaint filed by the woman on Wednesday.
The actress made the allegations in Bangalore when Karthik was getting engaged to another woman at Kushalnagar, 300 km from the state capital.
She first appeared on the sets of a local news channel on Wednesday evening and levelled the charges.
Later she went to the RT Nagar police station in Bangalore to launch a formal complaint with droves of TV crews in tow.
"She has filed a complaint in RT Nagar police station against Karthik Gowda, Sadananda Gowda's son, for allegedly raping and cheating her," Bangalore police commissioner MN Reddi said in Bangalore.
The woman alleged she was in a relationship with Karthik for several months and claimed that he wanted to have a physical relationship with her but she refused as they were not married.
She also claimed that Karthik married her in a temple on June 5 and that Sadananda Gowda and the rest of his family knew about the marriage.
"Now, without telling me he is getting engaged to another woman," she told Kannada TV channels.