This paper presents the results of tests on the weak form of Efficient Market Hypothesis applied to carbon efficient stock market indices of India, the United States of America (USA), Japan, and Brazil and their corresponding market indices which are used as their benchmark indices. In this study, Kolmogorov-Smirnov and Shapiro-Wilk tests are used to test the normality of data. Run test and auto-correlation test are used to check the randomness of the data. The tests are performed using daily closing prices for the whole sample period. It is found from the statistical tests that the daily closing prices do not follow random walks in all the four countries. However, monthly returns are following the random walk in case of India, USA, and Brazil, but not in case of Japan.