The National Weather Service Website should be able to help you. If you go to their website (www.weather.gov) and type in the zip code for a location in the upper left it will take you to the forecast page for that location. If you scroll to the bottom of that page and click on past weather information you can view the rainfall totals since January 1. Not sure if that is exactly what you need.
To see current rainfall totals on more of an hourly basis and not once a day when the above site updates check out http://aviationweather.gov/adds/metars/
Type in the METAR code for that station (if you don't know it it is in the station.txt file, link on the page). Type that in the box and then make sure you click the button for translated. That will tell you the hourly report for that weather station which, if there was rainfall, should say how much fell.