Cambridgeshire Police are reportedly investigating complaints about comments reportedly made on Twitter by BNP leader Nick Griffin about a gay couple from Huntingdon.
The MEP is alleged to have published the address of Michael Black and John Morgan on the social networking site and called for a demonstration to be held outside their home after they won a legal battle against a B&B owner who refused to let them share a double room.
A Cambridgeshire Police spokeswoman said:
"We have received a number of calls in relations to the tweets and are looking into the complaints we have received.
"Officers will also visit the men mentioned in the tweets as part of our inquiries."
One of the tweets included a home address, she added.