Uttarakhand was criticised for holding the festival, which attracted millions of people, during the pandemic.
Reports from different states suggested that those who returned from the festival ended up infecting a large number of people.
Unmasked crowds thronged the Kumbh festival in April even as several Indian cities grappled with a severe shortage of oxygen and hospital beds, reports the BBC.
At the time, officials said that every visitor was being screened for Covid. Private labs, based in Haryana and Delhi, were hired to conduct a majority of the tests.
But media reports last week alleged that these labs faked Covid reports to meet their daily testing quota.
The same phone numbers and addresses were used in hundreds of Covid reports.
"Orders have been issued to file a case against labs from Delhi and Haryana, which conducted testing at five places in Haridwar during Kumbh Mela," Subodh Uniyal, Uttarakhand government spokesperson, told ANI news agency.
The Kumbh Mela is the biggest Hindu festival - it draws people from all parts of India and the world. But experts had warned in March that the festival should be cancelled because of an impending second wave. But the government decided to go ahead, allowing people to visit from across the country.
Reports of fake Covid tests have also emerged from the northern state of Bihar where some primary healthcare centres have been accused of fudging data.