The Sea of Marmara is traversed by the North Anatolian Fault system and also presents abundant emission sites of methane gas into the water column. In order to assess the spatial relationship between gas emissions and active faults, the distribution of distances between gas emission sites and the nearest fault is calculated and compared with the distribution of distances between a uniform random distribution of points (Poisson process representing the null hypothesis of an absence of relationship between gas emissions and faults) and the nearest fault. Interestingly, the distance distribution for the Poisson process is nearly exponential, indicating that the fault map does not have a characteristic scale other than that representing the intensity of the fault network. The distance distribution for the observed gas emissions is significantly narrower than that arising from the Poisson process, with a Kolmogorov distance of 0.25 +/- 0.02. The crossing point between the two distributions defines the characteristic half-width of the swath of gas emission sites around the mapped active faults. For the whole Sea of Marmara data set a characteristic half-width of 900-1000 m is found which matches the half-width of the seafloor deformation zone observed around the main active fault. When the same analysis is applied to zones covering the Western High and the Central High it is found that the swath of gas emissions is wider on the Central High (2 km half-width), and not clearly related to the seafloor deformation zone there. This difference is put in perspective with recent work showing that creep is occurring on the western segment of the Main Marmara Fault (this also causing microseismicity) while the central Istanbul-Silivri segment may have remained locked since the 1766 magnitude 7+ earthquake. This suggests that aseismic slip (and not only earthquake occurrence) effectively maintains high permeability conduits in fault zones in sediments.