MiniBooNE reports the first absolute cross sections for neutral current single {pi}{sup 0} production on CH{sub 2} induced by neutrino and antineutrino interactions measured from the largest sets of NC {pi}{sup 0} events collected to date. The principal result consists of differential cross sections measured as functions of {pi}{sup 0} momentum and {pi}{sup 0} angle averaged over the neutrino flux at MiniBooNE. We find total cross sections of (4.76 {+-} 0.05{sub stat} {+-} 0.40{sub sys}) x 10{sup -40} cm{sup 2}/nucleon at a mean energy of <E{sub {nu}}> = 808 MeV and (1.48 {+-} 0.05{sub stat} {+-} 0.14{sub sys}) x 10{sup -40} cm{sup 2}/nucleon at a mean energy of <E{sub {nu}}> = 664 MeV for {nu}{sub {mu}} and {bar {nu}}{sub {mu}} induced production, respectively. In addition, we have included measurements of the neutrino and antineutrino total cross sections for incoherent exclusive NC 1{pi}{sup 0} production corrected for the effects of final state interactions to compare to prior results