A house neighbouring the plot has repeatedly been throwing dog mess onto one of the plots - which has caused one member to quit the plot and several to refuse to take it over.
The council has already been contacted and suggested the matter be reported to the police.
The committee has decided to involve local officers in a bid to resolve the issue.
The committee was told that recent attempts to install barriers had not been successful, and that fencing was now being investigated.
It is understood the problem has been occurring for some time.