We investigated the inertial and dissipation ranges of the reduced magnetic helicity spectrum of solar wind fluctuations and have found that this spectrum appears insensitive to solar cycle variations and changes in solar wind flow parameters. In the inertial range of the spectrum, the reduced helicity is large but random and independent of heliocentric distance between 0.3 and 10 AU. At small scales, in the dissipation range of the spectrum, a correlation appears to exist between the average value of the normalized reduced magnetic helicity and the polarity of magnetic sectors, suggesting that these fluctuations, if outward propagating, are predominantly right-hand polarized. In the inertial range the statistical properties of the normalized magnetic helicity are well approximated by a simple model of the magnetic field in which the total magnetic field vector randomly walks with only small variations in magnitude. The behavior of the inertial range spectrum is very similar to that seen in three- and two-and-a-half-dimensional simulations of the incompressible and compressible equations describing magnetohydrodynamic turbulence, consistent with the paradigm that the solar wind is a turbulent magnetofluid.