The Council may direct the city engineer to advertise for bids for construction of all or any part of the local improvement project on the basis of the approved report, before or after the passage of the resolution declaring the intent to form a local improvement district, before the public hearing on the proposed improvement, or at any time after the public hearing. No contract for the construction of the improvement may be entered into until after the public hearing has been held. When the proposed project is to be carried out in cooperation with any other governmental agency, the city engineer may adopt the plans, specifications, and estimates of the agency. Either agency may bid the project.