The Standards Board has been abolished.
I don't know the answer to the precise question, and am not sure it is worth pursuing. As I recall it, the legislation that created the Standards Board did specify that councils could not investigate breaches of standards or make judgements. But I assume that legislation is moribund, along with the Standards Board.
The practical answer is that a parish council has no jurisdiction over its members, not having any statutory power to make judgements or impose sanctions. So it is really a waste of time for a parish council to become involved in investigations.
Currently, the best course is to refer the matter to the principal authority, typically the district council. Although they don't have much power to do more than name and shame now. The only way things will go further is if a councillor is guilty of a criminal offence (where, once again, the parish council is not the appropriate investigating body).
