In a word, yes.  Most public agencies are required to award their public works construction projects to the lowest responsive, responsible bidder.  Failure to comply with public bidding requirements can result in a legal ruling which can void the contract.  However, there are also a variety of alternative project delivery methods (design-build, construction manager at-risk, job order contracting, public-private partnerships, lease lease-back etc.) that are available for select public agencies to use for qualifying projects.  The difficulty is that the statutes which authorize these alternative project delivery methods are not organized in any logical fashion.  I recently prepared a paper summarizing the main alternative project delivery methods available to public agencies in California, with a chart at the end that provides statutory references.  The paper was included with the materials at the Integrated Project Delivery Seminar Series.  In addition, the paper was included with the materials at the Lean in Public Sector Construction Projects Workshop and served as the basis for a presentation I gave on the topic.  You can view a copy of the paper by clicking here