Don't crush it or try to cut it.
If it is serpentine, serpentine contains the deadly mineral chyrsotile asbestos, a known carcinogen, exposure to which increases the risk of cancer mesothelioma.”
Where's it from?
Green is a common color for the Franciscan Cherts that outcrop along the US Pacific Coast, for example.
Has the attributes you describe ... smooth, cold, and heavy ... also, very hard compared to serpentine.
I think you may have a type of chert.