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Modern remote-sensing retrievals often invoke a Bayesian approach to infer atmospheric properties from observed radiances. In this approach, plausible mean states and variability for the quantities of interest are encoded in a prior distribution. Recent developments have devised prior assumptions for the correlation among atmospheric constituents and across observing locations. This work formulates a spatial statistical framework for simultaneous multi-footprint retrievals of carbon dioxide (CO2) with application to the Orbiting Carbon Observatory-2/3 (OCO-2/3). Formally, the retrieval state vector is extended to include atmospheric and surface conditions at many footprints in a small region, and a prior distribution that assumes spatial correlation across these locations is assumed. This spatial prior allows the length-scale, or range, of spatial correlation to vary between different elements of the state vector. Various single- and multi-footprint retrievals are compared in a simulation study. A spatial prior that also includes relatively large prior variances for CO2 results in posterior inferences that most accurately represent the true state and that reduce the correlation in retrieval error across locations.