You Were Meant for Me (1961)

Luo Ya-nan and Liang Ai-lun grow up together and never stop teasing each other. Liang, a doctor by profession, has a crush on the nurse Gao Shi-wen. To torment Liang, Luo dresses up as a man, and goes to the hospital to woo Gao. She wins Gao's heart, but also finds herself falling for the nurse's elder brother Zhuoran. So she introduces him to her 'twin sister', and Zhuoran duly falls in love with her. Now Luo finds herself dressing sometimes as a man and other times a woman, running back and forth between Gao and Zhuoran.