Omar, the working President of opposition National Conference, said a CID person was posted outside his residence to keep a watch on people coming and going out.
"Mufti Govt brazenly spying on me. A journalist interviewing me for a national daily just got stopped right outside my gate by CID person," he tweeted.
"She (journalist) was asked who she was and what the purpose of her visit was! Seriously guys if you want to know just ask me, I couldn't care less if you do," he added.
PDP rejected the accusation, saying Abdullah is levelling the allegation just to "make news", and hit back by charging him of spying on PDP president Mehbooba Mufti and other leaders when he was the Chief Minister.
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Waheedur Rehmaan Parra, PDP leader and political advisor to the Chief Minister, said, "It was not a cop who had questioned the journalist outside the residence of Omar Abdullah. It was a National Conference worker who was denied entry to Omar's residence who had asked a few questions to the lady."
Police also issued a statement, saying it is following the procedures and protocols as laid down in respect of all SSG (Special Security Group) protectees which includes Omar.
"In the context of views expressed in the social media by former Chief Minister Omar Abdullah, it is clarified that the procedures and protocols as laid down in the 'Blue Book' are being followed in respect of all SSG protectees including the former Chief Minister," a police spokesman said here.
"We do not even spend a second about what he is doing. He has made this unfortunate statement as he only wants to make news .... He (Abdullah) tweets and that is what he did during his six years (as Chief Minister)," he said.
Parra levelled counter allegations, saying during Omar Abdullah's tenure, "He used to spy on PDP president and other leaders of our party. We know what he does.