Can I install CCTV in common areas to prevent false allegations?

I live in Faridabad, Haryana. In my building, each floor belongs to a separate owner. I live on the 2nd floor, and there's no one above me. My 2nd-floor neighbor, due to longstanding animosity, lodged a false complaint, alleging that my father abused his wife while going down the common staircase. Our neighbor had threatened us in the past, so two years ago, I installed CCTV cameras above my door and on my rooftop. Can CCTV cameras be installed in other sections of the common staircase without compromising anyone’s privacy, so we can refute future false allegations? I’m okay with making the footage accessible to all three residents of the building.