  The Rotation powered pulsars Crab, Vela and Geminga have double peaked folded
light curves (FLC) at $\gamma$-ray energies, that have an approximate
reflection symmetry. Here this aspect is studied at soft X-ray energy by
analyzing a high resolution FLC of the Crab pulsar obtained at $1 - 10$ keV
using the {\it{NICER}} observatory. The rising edge of the first peak of the
FLC and the reflected version of the falling edge of the second peak are
compared in several ways, and phase ranges are identified where the two curves
are statistically similar. The best matching occurs when the two peaks are
aligned, but only in a small phase range of $\approx 0.0244$ just below their
peaks; their mean difference is $-0.78 \pm 1.8$ photons/sec with a reduced
$\chi^2$ of $0.93$. If the first curve is convolved by a Laplace function, the
corresponding numbers are phase range of $\approx 0.0274$, mean difference of
$-1.23 \pm 1.30$ and $\chi^2$ of $0.76$. These phase ranges are much smaller
than those over which the reflection symmetry has been perceived. Therefore the
only way the two edges can have a mirror relation over a substantial phase
range is if one invokes a broad and faint emission component of amplitude
$\approx 100$ photons/sec and width $\approx 0.1$ in phase, centered at phase
$\approx 0.1$ beyond the second peak.
