Kuldeep Singh Sengar, 50, from the ruling Bharatiya Janata Party (BJP) is accused of raping a 16-year-old girl last year – an allegation he denies.
The victim tried to kill herself last week in front of the chief minister’s home after alleging that the police had refused to register her case.
Her father died last week after clashes with Mr Sengar’s supporters.
It is not clear if and when the lawmaker will be arrested.
The police in the northern Indian state said the Central Bureau of Investigation would take a call on when to arrest him.
Activists say the allegations against Mr Sengar are very serious and he should have been arrested immediately.
The victim’s family has alleged that the lawmaker continued to threaten them and demand they withdraw the case, and that the state administration refused to take action.
The victim’s father was arrested last week after a clash with the supporters of the lawmaker.
But he died in a local hospital in Unnao district where he was taken for treatment from jail.
The family alleged that the lawmaker’s brother beat him and was responsible for his death.
The police arrested Atul Singh Sengar after outrage on social media and protests from the family.
Scrutiny of sexual violence in India has grown since the 2012 gang rape and murder of a student on a Delhi bus.
However, brutal sexual attacks against women and children continue to be reported across the country.