Kidangi C Sylvia was produced before a court here which remanded her to judicial custody till January 4, they said.
According to Police, Sylvia had accompanied her father Kidangi M Antony, who had kidney ailment, when he came to India for treatment at a private hospital here last year.
Her father had gone back to Congo on November 23, 2011 after treatment. Sylvia continued to stay in India though her visa expired on September 4, 2012.
On information from a lodge owner in Nagercoil in neighbouring Kanyakumari district that a foreign national was staying in his premises, Police verified her travel documents and found she was over staying.
As part of routine check, police had sought information about foreigners staying in hotels and lodges across the state.
The woman arrested under the Passport Act, was remanded to judicial custody, police said.
