"We have registered a case and have some leads which we are working on", SSP Kuldeep Singh Chahal said.
Verma was returning home accompanied by a friend and a bodyguard from an event at Chandigarh's Elante mall.
At around 4 am a few hours after the shooting, Dilpreet Singh Dhahan, a local gangster, took to social media to claim responsibility for the shooting. The two were admitted to a multi-specialty hospital in Mohali.
Parmish Verma had shot to fame with the single Gaal Ni Kadni that made him quite an icon in the Punjab pop music culture. As per a Hindustan Times report, the two were now undergoing treatment in Fortis hospital in Mahali and were said to be out of danger.
Dhahan's Facebook post read, "Mein dilpreetsinghdhahansariya nu dasnachaunda k ajjparmishverma de goliyabazianapamariya(I, Dilpreet Singh Dhahan, want to tell everyone that I am behind the shooting of Parmish Verma)".
In the post, the gangster also said the singer had a choice of whether he wanted to "listen to others". Dhahan had uploaded a status on his Facebook account with a picture of himself holding a pistol with Verma's picture with a cross drawn on it next to it. The post has been shared over 1,100 times.
The gangster's motive to claim responsibility for the shooting was unclear.
Verma is likely to be provided police protection following the attack. Police also claim that Dilpreet took to crime to avenge an assault in the village, but now has links with the Vicky Gounder gang.
Police have started the investigation.
While Verma and his friend were injured in the attack, they managed to speed away from the spot.
His another hit party number "Gaal Ni Kadni", released previous year, has over 118 million views on YouTube.