Unemployed Clifford Baddeley, aged 49, of Holehouse Road, Abbey Hulton, who is a BNP member, was arrested last month on suspicion of possessing cannabis.
Days later, police also searched the semi-detached house he shares with his wife Melanie.
She is a BNP city councillor who is standing as the party's Parliamentary candidate for the Stoke-on-Trent North constituency.
Mr Baddeley has not been charged with any offences, but remains on police bail while officers complete their investigation.
His wife said yesterday that she was aware of her husband's arrest, but had not told party chiefs about the situation.
The Abbey Green ward member said: "I haven't told the party, because it's nothing to do with me; it's his problem, not mine. I was very upset and annoyed with him when I found out about his arrest, and I still am because I wasn't aware what was happening at the time.
"He is on police bail at the moment and the police did come and search my house, but didn't find anything."
She added: "My husband did smoke cannabis for medical reasons, but as far as I'm concerned, I'm carrying on as normal with my election campaign."
Mr Baddeley admitted that he used to smoke the drug to relieve the pain of chronic arthritis.
He said: "I know that the BNP disapproves of drug use, but I'm more worried about my wife, who is very anti-drugs.
"She works tirelessly for this community, and it's embarrassing for her that I'm in this situation.
"I've stopped using cannabis, and I'm back on medication, although it doesn't work as well."
Stoke-on-Trent City Council's BNP group leader, Councillor Michael Coleman, was shocked to learn of Mr Baddeley's arrest.
But he said the party would still be backing Mrs Baddeley in the run-up to the General Election.
After being contacted by The Sentinel yesterday, he said: "It is shocking and disappointing. Mr Baddeley is a party member.
"I know he has a serious medical problem and is in pain, and that's why he used cannabis. But I don't approve, and the party doesn't approve of people using drugs in that way.
"We condemn these drugs in our communities and we have to condemn this. However, Melanie didn't know about it and we feel it doesn't affect her.
"It will be damaging for us to some degree, but we like Melanie and will be backing her."
Mrs Baddeley was unveiled as the BNP's Parliamentary candidate in Stoke-on-Trent North in January, when party leader Nick Griffin travelled to the city to unveil his election manifesto in Meir.
Staffordshire Police declined to comment on the investigation.
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