The notice asked Ritabrata Banerjee to turn up before CID officers on Friday, Additional Director General of Police, CID, West Bengal, Rajesh Kumar told news agency Press Trust of India.
The woman, who is a resident of Balurghat, has lodged a complaint at Balurghat police station in south Dinajpur district alleging that Ritabrata Banerjee had established physical relationship with her by promising marriage.
Last week, she had tweeted that Ritabrata Banerjee had promised to marry her before getting physical.
In another tweet addressed to Chief Minister Mamata Banerjee, she had sought her help in "fighting" her "battle" against Ritabrata Banerjee.
Ritabrata Banerjee has claimed that the woman's allegations were false and has lodged a complaint at Garfa police station in the city, demanding action against her for "maligning" his image, a senior officer of Kolkata Police said today.
The CPI-M had recently expelled Ritabrata Banerjee, who was the party's Rajya Sabha MP, for "gross anti-party activity" and breaking the party's discipline.