  [Abbreviated] We present an analysis of the newly identified $\mu$ Tau
Association (MUTA) of young stars at $\sim$ 150 pc from the Sun that is part of
the large Cas-Tau structure, coeval and co-moving with the $\alpha$ Persei
cluster. We identify more than 500 candidate members using Gaia DR2 data and
the BANYAN $\Sigma$ tool (Gagn\'e et al. 2018) and we determine an age of $62
\pm 7$ Myr for its population based on an empirical comparison of its
color-magnitude diagram sequence with those of other nearby young associations.
The MUTA is related to the Theia 160 group of Kounkel & Covey (2019) and
corresponds to the e Tau group of Liu et al. (2020). As part of this analysis,
we introduce an iterative method based on spectral templates to perform an
accurate correction of interstellar extinction of Gaia DR2 photometry, needed
because of its wide photometric bandpasses. We show that the members of the
MUTA display an expected increased rate of stellar activity and faster rotation
rates compared with older stars, and that literature measurements of the
lithium equivalent width of nine G0 to K3-type members are consistent with our
age determination. We show that the present-day mass function of the MUTA is
consistent with other known nearby young associations. We identify WD 0340+103
as a hot, massive white dwarf remnant of a B2 member that left its planetary
nebula phase only 270,000 years ago, posing an independent age constraint of
$60_{-6}^{+8}$ Myr for the MUTA.
