Hi Sultan,  you cannot ...

Hi Sultan,  you cannot stipulate that the data must be normally distributed - you must use the data that you have and assess what distribution pattern best fits it.  This then governs the regression analysis you will apply.  You are on track with applying a regression analysis and checking for level of significance.  If you have a number of rainfall and weather stations and streamflow gauges in the same catchment, you will also need to test for cross correlation.  I did this many years ago and modeled the system with a stochastic model.  The other option is using a deterministic model approach.  There are some off-the-shelf models you can use now days, but I am not familiar with them.