We carry out a systematic study of the density structure of gas in the Central Molecular Zone (CMZ) in the Galactic center by extracting clumps from the APEX Telescope Large Area Survey of the Galaxy survey at 870{mu}m. We find that the clumps follow a scaling of m={rho}_0_r^3^, which corresponds to a characteristic density of n_H_2__=1.6x10^3^/cm^3^ ({rho}_0_=112M{sun}/pc^3^) with a variation of ~0.5dex, where we assumed a gas-to-dust mass ratio of 100. This characteristic density can be interpreted as the result of thermal pressure equilibrium between the molecular gas and the warm ambient interstellar medium. Such an equilibrium can plausibly be established since shear has approximately the same strength as self-gravity. Our findings may explain the fact that star formation in the CMZ is highly inefficient compared to the rest of the Milky Way disk. We also identify a population of clumps whose densities are two orders of magnitudes higher in the vicinity of the Sgr B2 region, which we propose are produced by collisions between the clumps of lower densities. For these collisions to occur, processes such as compressive tides probably have created the appropriate condition by assembling the clumps together.