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It doesn't look like you can define the Site:Precipitation object's parameters in the Openstudio interface. The available methods to add this to your building energy modeling project are:

1. Export the IDF (EnergyPlus input file) from OpenStudio, add the Site:Precipitation object to the exported IDF, then run the IDF directly in EnergyPlus. This requires more work, doesn't allow you to view OpenStudio results (monthly bar charts of energy use, zone conditions summary, etc.), and should only be done if you are done with setting all input parameters in OpenStudio. If you update a parameter in OpenStudio, you have to redo the export IDF and add precipitation object process.
2. Use a measure. There are three categories of measures: OpenStudio, EnergyPlus, and Reporting. You can use an OpenStudio measure if the object you want to add or change is in the OpenStudio SDK. It does not look like the Site:Precipitation object is part of the SDK. In this case, you will need to use an EnergyPlus measure to "inject" the Site:Precipitation object into the model when you simulate.

There is a free resource managed by NREL (developers of OpenStudio) called the Building Component Library. You can search here to see if there is an existing measure you can download and use. Unfortunately for you, no measures are found if you search for "precipitation" or "rain". So, it looks like you will need to write your own EnergyPlus measure to add precipitation if you want to use method 2 instead of method 1 outlined above. Which sounds like the case, from your original post.