A combination of different statistical methods and flow duration curves was used to examine hydraulic connection between the Plitvica stream and the surrounding piezometers that capture the groundwater of the Varaždin alluvial aquifer. Also, rainfall quantities over a wider study area were considered to examine the effect of precipitation on Plitvica water levels and groundwater levels. The following statistical methods were used in this paper: the correlation method, the auto-correlation method, and the cross-correlation method. Correlation analysis show that there is generally a significant correlation between the Plitvica water levels and groundwater levels, with positive direction of the correlation. The analysis of auto-correlograms for groundwater and surface water shows that the correlation coefficient value drops below 0.2 after a longer period, which indicates a long-term memory of the system that can be explained by the slow flow and thus slow pressure transfer. Cross-correlation analyses of the time series of the Plitvica water levels and groundwater levels showed a time lag of 1–2 days with a fairly significant cross-correlation coefficient. For precipitation and groundwater levels, the relationship is much weaker, with a lag time of 4–5 days with a weak cross-correlation coefficient. The least time lag, within a day, was established between precipitation and Plitvica water levels. Analyses of the flow duration curves revealed that Plitvica almost completely drains groundwater, except in the vicinity of the piezometer 2178 where Plitvica recharges the aquifer about a quarter of the time.