Existing observations are consistent with rich clusters of galaxies having no dust on $\simgt$ Mpc scales, while galaxy groups most probably do have dust distributed over $\lesssim$ Mpc scales. Dust in groups accounts for the observed redshift asymmetries of their galaxy distributions, and about $E(B-V)∼ 0.1-0.2$ mag of reddening. Motivated by these results, we develop a new technique for determining the degree of reddening and extinction due to widely-distributed dust in nearby moderately rich and poor galaxy clusters. The method compares the color-magnitude plane distributions of galaxies from cluster and control regions on the sky, where control regions are assumed to be unaffected by dust. The method is statistical in nature; it can distinguish between uniformly, non-uniformly, and clumpily distributed dust, and can determine the amount of reddening and obscuration without a priori assuming an $A_R/E(B_{J}-R)$ ratio. We apply the method to nearby, $z \le 0.08$, medium rich and poor APM galaxy clusters. We detect no dust in these on 1.3 Mpc scales (we assume $h = 0.75$), and derive 99% confidence upper limits on extinction of $A_{R} = 0.025 $ and reddening of $E(B_{J} - R) = 0.025 ($which corresponds to $E(B - V) ≈ 0.02)$. We test the method using clusters whose galaxies have been artificially reddened and obscured by various amounts, and conclude that it robustly recovers the input values for reddening, its distribution, and the ratio of total-to-selective extinction. The method can be applied to any set of galaxy clusters or groups constructed out of homogeneous and uniform two-color galaxy catalogs. ; Comment: 19 Pages total, including 6 encapsulated postscript figures. Accepted for publication in the June 2003 issue of the Astronomical Journal