The Aedes aegypti mosquito is the main vector of dengue and is an extremely synanthropic insect and due to its anthropophilic nature, it has specific reproductive needs. In addition to that, it also needs tropical regions that provide climate-prone conditions that favor vector development. In this article, we propose the cross-correlation analysis between the climatic variables air temperature, relative humidity, weekly average precipitation and dengue cases in the period from 2017 to early 2021 in the municipality of Alagoinhas, Bahia, Brazil. To do so, we apply the trend-free cross-correlation, $\rho DCCA$, being a generalization of the fluctuation analysis without trend, where we calculate the cross correlation between time series to establish the influence of these variables on the occurrence of dengue disease. The results obtained here were a moderate correlation between relative humidity and the incidence of dengue cases, and a low correlation for relative air temperature and precipitation. However, the predominant factor in the incidence of dengue cases in the city of Alagoinhas is relative humidity and not air temperature and precipitation.