The color blue is likely derived from so-called government blue books, official publications printed by a government (such as that of a state) describing its organization, and providing a list of contact information. (The blue pages published in a printed telephone directory is usually quite abridged, compared to official blue books).
The color blue is probably derived from the term "blue book," referring to official publications issued by governments, detailing their structure and offering contact details. In contrast, the blue sections found in phonebooks are typically much shorter than these official documents.