How can we predict if it's raining, drizzling or there is snow fall by using precipitation intensity (inches/hour)?
TL;DR: When reporting precipitation types, we still have to manually look out the window.

TL;SR: You do not mention how the information is gathered, so I will go over the different ways.

The first and most obvious one is the air temperature.  If the air temperature is above freezing then you have rain, below you have snow.  Until recently reporting stations were all manned, and so someone would go out and look and determine what kind of precip is falling.  Reports such as if it was raining or snowing, cloudy or sunny, are based on the observation at that moment, not over the course of time.  With technology, a simple camera and light source can determine precip type.  Snow reflects light back to the camera whereas rain lets the light pass through the drop.

Radar is a little more complicated.  We now use what is known as Duel Polarization (Duel-Pol) radars.  Using signals polarized in different directions, we can measure the shape of the precipitation.

Wind resistance flattens out rain drops, making them wider than tall.  Hail tends to be round.  Snow may present itself on it's face appearing as hail, or side, appearing as rain.  The ratio of height to width gives the Spectral Differential Phase.  Snow has a lower value and rain has a higher value with some overlap.
Another important calculation is the Correlation Coefficient, which measures how similarly the two polarizations interact with the precip.  In the image below is a map of different precip types and their CC.  Note that snow has a much wider range of values than snow.  Snow type is determined by temperature, wet snow closer to freezing, drier snow as you get colder.


These and other calculations give on the fly estimations for precipitation type.

However, what you see on the radar on TV still uses the old way of mapping station reported temperatures onto the radar screen.  On this rain/snow radar loop You can make out the rain in green and yellow, the mix precip in pink, and snow in blue.  Note however the mix line (where the air is at 32°F/0°C, moves five times over the 10 frames, and it is not smooth.  This line is calculated by the measured temperatures from weather stations scattered over the area, drawing a line that marks the freezing point, much like drawing terrain contours.  While the radar updates every 10 minutes, weather stations are only sampled hourly or quarterly.

So without knowing the exact way your data was gathered, I would say someone stuck their head out the window and marked on the computer that it was rain.

Extra reading: 
http://www.nssl.noaa.gov/tools/radar/dualpol/
https://www.weather.gov/media/lmk/soo/Dual_Pol_Overview.pdf
http://training.weather.gov/wdtd/courses/dualpol/documents/DualPolRadarPrinciples.pdf