  In a previous paper (Maoz et al. 1999), we reported a Hubble Space Telescope
(HST) Cepheid distance to the galaxy NGC 4258 obtained using the calibrations
and methods then standard for the Key Project on the Extragalactic Distance
Scale. Here, we reevaluate the Cepheid distance using the revised Key Project
procedures described in Freedman et al. (2001). These revisions alter the zero
points and slopes of the Cepheid Period-Luminosity (P-L) relations derived at
the Large Magellanic Cloud (LMC), the calibration of the HST WFPC2 camera, and
the treatment of metallicity differences. We also provide herein full
information on the Cepheids described in Maoz et al. 1999. Using the refined
Key Project techniques and calibrations, we determine the distance modulus of
NGC 4258 to be 29.47 +/- 0.09 mag (unique to this determination) +/- 0.15 mag
(systematic uncertainties in Key Project distances), corresponding to a metric
distance of 7.8 +/- 0.3 +/- 0.5 Mpc and 1.2 sigma from the maser distance of
7.2 +/- 0.5 Mpc. We also test the alternative Cepheid P-L relations of Feast
(1999), which yield more discrepant results. Additionally, we place weak limits
upon the distance to the LMC and upon the effect of metallicity in Cepheid
distance determinations.
