However, she said her government has been apprehensive as the CBI had "messed up" the Aarushi Talwar murder case in Noida.
"If the family of the victim wants a CBI or any other inquiry my government has no objection to it. The only fear is that in the case of CBI inquiry the probe may get messed up like in the Aarushi murder case," she said.
Condemning the incident in which a 14-year-old girl was allegedly raped and murdered inside a police station, the chief minister said she wanted to assure the family of the victim that sternest action would be taken against the guilty.
"Whenever any inhuman incident occurs against women, the Opposition should rise above party politics and help catch the culprits. They should not indulge in dirty politics," she said.
In a related development, the state government has suspended the then superintendent of police of Lakhimpur D K Rai, who had stated after the first post-mortem on the teenager that she had committed suicide and was not murdered. The second post-mortem has concluded that the girl was killed but not raped. The girl was found hanging in the premises of Nighasan police station in the district on Friday.
Accusing the Centre of indirectly politicising government commissions, she said, "Other than UP, atrocities are taking place against Dalits across the country, but nowhere does the Centre send its commissions."
While atrocities against women and other crimes were taking place in Delhi, the commissions were not being allowed to carry out inquiries, she said.
"Despite the fact that all the commissions have their headquarters in Delhi, they are not being sent to inquire into cases of atrocities against women and other crimes by the Centre, because it has its own government," Mayawati alleged.
Coming down heavily on the previous state governments, Mayawati alleged, "Opposition parties during their rule produced professional mafias and criminals in large numbers for political gains... We have inherited this evil."
On the Lokpal bill, the chief minister suggested that members of the civil society should create awareness among people if they want the bill to incorporate certain proposals suggested by them.
