The Small Magellanic Cloud (SMC) is an ideal laboratory for studying the properties of star-forming regions thanks to its low metallicity, which has an impact on the molecular gas abundance. However, a small number of molecular gas surveys of the entire galaxy have been carried out in the last few years, limiting the measurements of interstellar medium (ISM) properties in a homogeneous manner. We present the CO(3-2) APEX survey at a 6pc resolution of the bar of the SMC, observed with the SuperCAM receiver attached to the APEX telescope. This high-resolution survey has allowed us to study certain properties of the ISM and to identify CO clouds in the innermost parts of the H_2_ envelopes. We adopted the CO analysis in the SMC bar comparing the CO(3-2) survey with that of the CO(2-1) of a similar resolution.We studied the CO(3-2)-to-CO(2-1) ratio (R32), which is very sensitive to the environment properties (e.g., star-forming regions). We analyzed the correlation of this ratio with observational quantities that trace the star formation such as the local CO emission, the Spitzer color [70=160], and the total IR surface brightness measured from the Spitzer and Herschel bands. For the identification of the CO(3-2) clouds, we used the CPROPS algorithm, which allowed us to measure the physical properties of the clouds. We analyzed the scaling relationships of such physical properties. We obtained R_32_=0.65+/-0.02 for the SW bar and a slightly higher ratio, R_32_=0.7+/-0.1; for N66 in the SMC.We found that R_32_ varies from region to region, depending on the star formation activity. In regions dominated by HII and photo-dissociated regions (e.g., N22, N66) R_32) tends to be higher than the median values. Meanwhile, lower values were found toward quiescent clouds.We also found that R_32_ is correlated with the IR color [70/160] and the total IR surface brightness. This finding indicates that R_32_ increases with environmental properties, such as the dust temperature, total gas density, and radiation field. We identified 225 molecular clouds with sizes of R>1.5pc and signal-to-noise ratios (S/N) of >3, of which only 17 are well resolved CO(3-2) clouds with S/N>~5. These 17 clouds follow consistent scaling relationships to the inner Milky Way clouds but with some departures. For instance, CO(3-2) tends to be less turbulent and less luminous than the inner Milky Way clouds of similar sizes. Finally, we estimated a median virial-based CO(3-2)-to-H_2_ conversion factor of 12.6^+10^_-7^M_{sun}_ (K.km/s/pc^2^)^-1^ for the total sample.