We report a sensitive search for the rotational transitions of the carbon chain alcohol HC4OH in the frequency range of 21.2-46.7 GHz in the star-forming region L1527 and the dark cloud TMC-1. The motivation was laboratory detection of HC4OH by microwave spectroscopy. Despite achieving rms noise levels of several millikelvin in the antenna temperature using the 45 m telescope at Nobeyama Radio Observatory, the detection was not successful, leading to 3 sigma upper limits corresponding to the column densities of 2.0 times 1012 and 5.6 times 1012 cm-2 in L1527 and TMC-1, respectively. These upper limits indicate that [HC4OH]/[HC5N] ratios are less than 0.3 and 0.1 in L1527 and TMC-1, respectively, where HC5N is an HC4-chain cyanide and HC4OH is a hydroxide. These ratios suggest that the cyano carbon chain molecule dominates the hydroxyl carbon chain molecule in L1527 and TMC-1. This is contrary to the case of saturated compounds in hot cores, e.g., CH3OH and CH3CN, and can be a chemical feature of carbon chain molecules in L1527 and TMC-1. In addition, the column densities of the unsubstituted carbon chain molecule C4H and the sulfur-bearing molecules SO and HCS+ were determined from detected lines in L1527.