Commentary
The issue here is whether the teacher was complaining about a parent, who was also a governor at the school, or complaining about the person in their role as a governor, who was also a parent at the school. These are two very distinct situations and would be dealt with differently.
If it was the former, the school’s complaints procedure should not be applied, as staff are unable to complain about the actions of parents. There would have been no need for the Chair to get involved in the matter.
If it was the latter, then the Chair (or another governor) investigates the complaint against the governor using the school’s complaints procedure.
If staff have concerns about the behaviour of parents, they should in the first instance, go to their line manager or headteacher to discuss. It may well be that the line manager or head can act as mediator between the parent and the member of staff to resolve any issues. If the relationship is still difficult between the parent and the teacher, then any future concerns the parent may have, could be directed to the school’s complaints officer or headteacher to resolve.
A parent can however, complain about the conduct of a teacher, and this will usually be investigated by a relevant member of staff, or the headteacher.
Even if the process used in this case may not have been the right process, and whilst the Chair indicates that the situation is not fully resolved, it would appear that the issue had been dealt successfully, with the Chair dealing with it fully and sensitively with both parties. Above all, it is so important to deal with any concerns or complaint as soon as possible to avoid any further escalation and stress for all parties concerned.
Further Information about school complaints can be found in this useful guidance:
School Governor Reflections Resource 
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