In Canada, sky-cloudiness (or cloud cover) condition is reported in terms of tenths of the sky dome covered by clouds and hence has 11 categories (0/10 for clear sky, 1/10 for one tenth of the sky dome covered by clouds, …, and 10/10 for overcast). The cloud cover data often contain temporal discontinuities (changepoints) and present a large amount of observational uncertainty. Detecting changepoints in a sequence of continuous random variables has been extensively explored in both statistics and climatology literature. However, changepoint analyses of a multinomial sequence data with extra variabilities are relatively sparse. This study develops a likelihood ratio test for detecting a sudden change in parameters of the cumulative logit model for a multinomial sequence. The extra-multinomial variation is accounted for by allowing an overdispersion parameter in the model fitting. Moreover, the empirical distribution of the estimated changepoint is approximated by a bootstrap method. An application of this new technique to real sky cloudiness data in Canada is presented.