The Congress said it would continue to mount pressure on the state government to recommend a Central Bureau of Investigation (CBI) inquiry into the arson case.
Abidi and BSP legislator Jitendra Singh have been accused of arson and vandalism at Joshi's residence in Lucknow. A police report has been registered against them on a complaint by the Congress.
Joshi's house in Lucknow was set on fire Wednesday night allegedly by a group of BSP workers because she made remarks that offended Mayawati both as a woman and a Dalit.
Joshi was arrested early Thursday and charged under the Scheduled Castes and Scheduled Tribes (Prevention of Atrocities) Act. She was granted bail by a Moradabad court Saturday.
Joshi has already apologised for her remarks and demanded that the probe into the arson attack on her house be conducted by the CBI.