The petition, filed by a group of persons describing themselves as BJP supporters, sought a direction to the BJP and the Shiv Sena to stand by their pre-poll alliance and form government.
Advocate Mathews Nedumpara, their lawyer, on Thursday approached two different benches of the high court seeking urgent hearing, as Thackeray is slated to take oath of office in the evening.
But both the benches refused to take up the plea for urgent hearing.
A division bench of Justices S C Dharmadhikari and R I Chagla said they do not have time.
Nedumpara then approached the division bench of Chief Justice Pradeep Nandrajog and Justice Bharati Dangre, contending that Thackeray's swearing-in was "unconstitutional and void".
When the bench asked him why, the lawyer contended that the BJP and Sena betrayed the trust of voters, and the two parties should stand by their alliance sealed before the Assembly elections.
To this, Chief Justice Nandrajog said, "Is the concept of divorce new to the law of marriages?
"When the appropriate bench has already refused to take the petition for hearing today, then why should we take up," the judges said.
The petition claimed that the Shiv Sena, Congress and NCP, who stitched up a post-election alliance only to form government, acted in an "immoral and unethical" manner.
The petitioners were BJP supporters and had voted for Sena candidates only because of the pre-poll alliance between the two parties, it said.
"Several voters including the petitioners voted for BJP and Shiv Sena because they disapprove of the policies and ideology of Congress and NCP," the plea said, seeking an interim stay to the swearing-in of Thackeray as CM.
It also sought a declaration that the Sena, NCP and Congress, in forming a coalition, had betrayed people's mandate.
The petition has been filed by Rohini Amin, Mohit Amin, Rajesh Adrekar, Danesh Jain, Sunil Gupta, Ramanathan Laxmanan, Dipti Thakkar and Kanchan Rochlaney.