The relationship between the high Galactic latitude molecular clouds (HLCs) and associated atomic hydrogen gas is investigated. In a global study, we examined a total of 75 HLCs observed in the CO (J = 1-0) transition and found that all the HLCs are associated with H I gas in bath position and velocity with most of the HLCs located along filamentary or looplike H I structures. A small-scale comparison, using Green Bank 43 m H I data toward 10 regions associated with 18 HLCs, shows that the positions of the CO and H I peaks are typically offset from one another by similar to 1.degrees 5, comparable to the linear size of the HLCs. No obvious pattern for these CO-H I offsets was found either in relation to the Galactic plane or to an arbitrary explosion center. Typical velocity dispersions of the CO and its associated H I are found to be 0.6 and 3.0 km s(-1), with a mean H I/CO linewidths ratio of 5.7, which is close to the square root of the ratio of mass of CO/H I possibly indicating energy equipartition between the two phases. The data suggest that the molecular clouds condensed from the atomic gas in situ, rather than having been entrained in the H I. Moreover, the data are consistent with formation from the H I by means of a phase transition in pressure equilibrium. A few cloud complexes are anomalous, perhaps indicating variants in how the clouds formed. We find a minimum total hydrogen column density of 5 x 10(20) cm(-2) and a minimum relative abundance of H-2 nucleons of 50% in the 18 clouds we observed. Two of the 10 observed H I clouds, those associated with the molecular clouds MBM 27-29 and MBM 53-55, show clear arclike structures and the latter appear to be expanding with a velocity of about 18 km s(-1). The kinetic energy of this expanding shell is estimated to be about 4 x 10(49) ergs, consistent with having been produced as a result of a supernova explosion or a stellar wind.
