While the policy does not require the city to work exclusively with union shops, PLA opponents are concerned it limits their ability to bid on certain work.
The city and borough ended Fiscal Year 2013 with about $9.5 million in fund balance, $1.2 million more than projected.
Assembly members want the city's Docks & Harbors Department to reconsider a recent decision to bid a project without a PLA.
Kalibo is the capital of the Philippine province of Aklan.
Assembly members Mary Becker and Karen Crane were also sworn in to their second terms on the CBJ Assembly before Monday's meeting.
Kate Troll will be sworn in and outgoing Assembly member Johan Dybdahl will be recognized for his service.
City Clerk Laurie Sica says the CBJ Canvass Board met Tuesday to complete its review of absentee and questioned ballots.
In unofficial results, Troll leads by almost 300 votes with 1866 total; Bill Peters has 1571 votes.
She's running unopposed for a second term to a District 1 seat
Karen Crane is running unopposed for a second term on the CBJ Assembly. She says there are unfinished projects she wants to complete and still likes working on the major issues facing the city.