Detectives are investigating whether the article, published in July's edition of The Watchtower, is in breach of Britain's religious hatred laws.
The article, published in the magazine which is distributed by Jehovah's Witnesses across the globe, reportedly warned followers to avoid "false teachers" which it condemned as being "mentally diseased".
"Suppose that a doctor told you to avoid contact with someone who is infected with a contagious, deadly disease," part of the article stated.
"You would know what the doctor means, and you would strictly heed his warning. Well, apostates are 'mentally diseased', and they seek to infect others with their disloyal teachings."
A group of former Witnesses, based in Portsmouth, have made an official complaint to Hampshire Police about the article. Police have launched an investigation.
They are considering whether to complain to the Charity Commission. The Watchtower Bible and Tract Society of Britain, which prints church doctrine in Britain, is a registered charity.
The church is known for handing down harsh punishments to followers who criticise doctrines or raise questions about the faith.
Angus Robertson, a former Witness "elder" from an undisclosed town in Hampshire, who was present at the meeting with police, told The Independent: "The way scripture is being used to bully people must be challenged.
"If a religion was preaching that blacks or gays were mentally diseased there would understandable outrage."
But Rick Fenton, a church spokesman, defended the passages, saying ostracisation was "a personal matter for each individual to decide for himself".
"Any one of Jehovah's Witnesses is free to express their feelings and to ask questions," he said. "If a person changes their mind about Bible-based teachings they once held dear, we recognise their right to leave."
A Hampshire police spokesman was unavailable for comment.