IMLS Public Libraries in the United States Survey 2010 Bar Graphs: Average Square Footage by Service Area Population, Top and Bottom 10

The top 10 states mapped
Note:  Maine's Portland Public Library is the state's only outlet in this population category.  Ditto for New Hampshire's Manchester City Library.  In addition, a significant majority of public libraries in Midwestern states are organized at the municipal level.

The bottom 10 states mapped

In their defense, Southern and Southeastern states -- Louisiana, Georgia, South Carolina, North Carolina, Virginia -- are more likely to large larger units of public library governance, i.e., few central facilities and more branches.  At a glance, though, I think these states would rank toward the bottom of a list of library square footage per capita.