The condition of the building used by Costa in Leyburn has prompted complaints.
The coffee shop opened in the former HSBC bank last year after it was put on the market for £220,000.
Although the ground floor was refurbished, the upper floors were not altered and vegetation is now growing on the building.
Concerns have also been raised about the amount of pigeon droppings on the building and the surrounding pavement.
The coffee shop closed in March due to the lockdown and has not yet reopened.
Leyburn mayor, Richard Sanderson, said the town council had attempted to contact the owners on several occasions but had not had a reply.
“We have sent several letters to the owners about the general condition of the building but I don’t think we’ve had a response.
“We’ve also mentioned to the staff in the cafe and they’ve said they would pass it on.
“The issue regarding the pigeon droppings wasn’t that bad when they were open because they would clean it up regularly but it obviously got worse since they’ve been shut.”
It is understood the branch is run by a Costa franchisee, Cuppacoff Limited, a company which runs a number of Costa shops across the country and is based in Wembley, London.
The firm also runs the Bedale branch which has reopened after Covid-19 restrictions have relaxed.
Richmondshire Today has contacted the franchisee about the premises but has not yet had a reply.