Sub Inspector Arshid Ashraf Mir at Khanyar area was shot twice from a close range in downtown Srinagar at around 1.40 pm.
While police is tight-lipped about the searches, it is believed that the raids were part of an investigation into a blog post that instigates people against the country, sources said.
Geelani died last Wednesday night at his residence in Srinagar after a prolonged illness.
Jammu and Kashmir Police also released four videos through its twitter handle to show that 91-year-old Geelani was laid to rest as per the rituals in the intervening night of September 1 and 2.
The FIR was filed against the family members for chanting anti-India slogans and draping Geelani’s body with a Pakistani flag.
The police informed that all three are associated with LeT Tanzeem and were involved in supporting terrorist activities.
The J&K administration on Sunday decided to stop security clearance for jobs and passports of Kashmiri youth allegedly involved in stone pelting and anti-national activities.
Incriminating material including hand grenades have been recovered from their possession, the spokesman said.
Ex-cop caught ferrying militants let off the hook while innocent Kashmiris rot in jails: Mehbooba Mufti
Mehbooba's remarks came after a copy of a government order dated May 20 dismissing Singh, a deputy superintendent of police, from service went viral on social media.
Digital evidence like CCTV footage, photographs, videos and audio clips, quadcopter images available in the records of the police, security forces, and security agencies be also referred.
Following information about a drone flying over the border belt of Kanachak along the International Border (IB) on Thursday night, a quick reaction team (QRT) of the police swung into action.
The alleged terrorists barged into the house of Constable Sajad Malik at Kokargund in Dooru area and opened fire at his wife, Nahida Jan, and daughter Madeeha, a police official said.
Police said they have taken cognisance of the matter and the circumstances of the incident are being looked into.
The team are conducting further searches and questioning inmates and jail staff about how mobiles and SIM cards reached inside the complex.
Preliminary investigation has revealed that they were providing shelter, logistics, and other material support to terrorists of LeT.