  In the presence of direct trajectories connecting source and drain contacts,
the conductance of a quantum dot may exhibit resonances of the Fano type. Since
Fano resonances result from the interference of two transmission pathways,
their lineshape (as described by the Fano parameter q) is sensitive to
dephasing in the quantum dot. We show that under certain circumstances the
dephasing time can be extracted from a measurement of q for a single resonance.
We also show that q fluctuates from level to level, and calculate its
probability distribution for a chaotic quantum dot. Our results are relevant to
recent experiments by Goeres et al.
