The Gay Police Association (GPA) is being investigated after it claimed a rise in homophobic attacks was due to religious belief.
An advert, showing a Bible next to a pool of blood under the heading "in the name of the father", appeared in a national newspaper's supplement.
Scotland Yard said the inquiry "centres on whether the advert constitutes a faith crime."
The GPA refused to comment while the matter was still under investigation.
The advert appeared in the Diversity supplement of the Independent newspaper on 29 June, two days ahead of the Europride gay and lesbian parade in London.
Public complaint
It stated: "In the last 12 months, the GPA has recorded a 74% increase in homophobic incidents, where the sole or primary motivating factor was the religious belief of the perpetrator."
The GPA was formed in 1990 and has members in all 52 UK police forces.
Scotland Yard said the inquiry was prompted by a complaint by a member of the public.
A GPA spokesman said they were aware police have received a complaint in relation to the advert.
"Until that investigation has been completed we're unable to comment further on this matter," said a spokesman.
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