The authority to choose and call a minister is a key part of congregational polity. Most congregations include a section in their bylaws that dictate basic constraints on the process:
Calling a Minister in Bylaws
Very few things that a congregation does affect it as greatly, or are as important, as the choice of a minister. Wonderful ministerial-congregational matches provide new life and purpose to an institution and help lead both parties well into the future….
During late January or February, and before meeting with the UUA’s Transitions staff, the governing board should review their bylaws, so they can determine if the UUA’s recommendations for a search team selection process will be compliant with your bylaws.
If there are unusual constraints, the UUA staff can be thought partners about how to address them. A congregation may choose to amend the bylaws before the search, if desired.