BEIJING—Activity in China’s services sector contracted at the sharpest pace in two years in March as a surge in coronavirus cases restricted mobility and weighed on demand, a private sector survey showed on Wednesday. The Caixin services Purchasing Managers’ Index (PMI) dived to 42.0 in March from 50.2 in February, dropping below the 50-point mark that separates growth from contraction on a monthly basis. The reading indicates the sharpest activity decline since the initial onset of the COVID-19 pandemic in February 2020. The survey, which focuses more on small firms in coastal regions, tallied with an official survey, which also showed deterioration in the services sector. Analysts say contact-intensive services sectors such as transportation, hotel, and catering were hurt the most, clouding the outlook for a much anticipated rebound in consumption this year. A sub-index for new business fell for a second consecutive month, and at the fastest pace since …