We present observations of the C-band 1_10_-1_11_ (4.8GHz) and Ku-band 2_11_-2_12_ (14.5GHz) K-doublet lines of H_2_CO and the C-band 1_10_-1_11_ (4.6GHz) line of H_2_^13^CO toward a large sample of Galactic molecular clouds, through the Shanghai Tianma 65m radio telescope (TMRT). Our sample with 112 sources includes strong H_2_CO sources from the TMRT molecular line survey at C-band and other known H_2_CO sources. All three lines are detected toward 38 objects (43 radial velocity components) yielding a detection rate of 34%. Complementary observations of their continuum emission at both C- and Ku-bands were performed. Combining spectral line parameters and continuum data, we calculate the column densities, the optical depths and the isotope ratio H_2_^12^CO/H_2_^13^CO for each source. To evaluate photon trapping caused by sometimes significant opacities in the main isotopologue's rotational mm-wave lines connecting our measured K-doublets, and to obtain ^12^C/^13^C abundance ratios, we used the RADEX non-LTE model accounting for radiative transfer effects. This implied the use of the new collision rates from Wiesenfeld & Faure. Also implementing distance values from trigonometric parallax measurements for our sources, we obtain a linear fit of ^12^C/^13^C=(5.08+/-1.10)D_GC_+(11.86+/-6.60), with a correlation coefficient of 0.58. D_GC_ refers to Galactocentric distances. Our ^12^C/^13^C ratios agree very well with the ones deduced from CN and C^18^O but are lower than those previously reported on the basis of H_2_CO, tending to suggest that the bulk of the H_2_CO in our sources was formed on dust grain mantles and not in the gas phase.