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This study used the standardized precipitation index (SPI) and the standardized runoff index (SRI) to analyze dry and humid conditions in the hill-country catchment area of the Laborec River (Slovakia) over a period of 50 years (1970–2019). Analysis of the SPI and SRI over various time scales showed the occurrence of wet periods (index > 1.0) that were associated with precipitation exceeding the long-term norm, and dry periods (index below −1.0), which were the result of small amounts of precipitation. Analysis of the correlation between the SPI and SRI on different time scales revealed that the catchment showed a weaker response to precipitation over short time scales (1 and 3 months) and a stronger response over longer accumulation periods (6, 9, and 12 months). The highest annual correlation coefficient (r = 0.72) was recorded between SRI-6 at the Humenne hydrometric station and SPI-9 at the Medzilaborce meteorological station in the upper part of the catchment area. The strongest annual correlation (r = 0.69) was obtained between the Izkovce and Kamenica stations in the lower part of the catchment area. As shown by the cross-relationships examined over different periods of accumulation of flows and precipitation, hydrological droughts appeared as a result of the occurrence of meteorological droughts with a three-month delay. The conducted analysis showed that in the case of the Laborec river catchment area, there was a strong correlation between the occurrence of meteorological drought and hydrological drought.