  In this paper, we establish a Whittaker-Plancherel inversion formula for
$\mathrm{SL}_2(\mathbb{C})$ from the analytic perspective of the Bessel
transform of Bruggeman and Motohashi. The formula gives a decomposition of the
Whittaker-Fourier coefficient of a compactly supported function on
$\mathrm{SL}_2(\mathbb{C})$ in terms of its Bessel coefficients attached to
irreducible unitary tempered representations of $\mathrm{SL}_2(\mathbb{C})$.
