TL;DR: No,does not cause hair fall.
Unless you are consuming something like 12+ cups of green tea a day, there should not be a physical effect as detrimental as hair fall as a result. On the contrary, green tea is known for its various health benefits due to the presence of antioxidants and other minerals. However, too much of anything is a bad thing and drinking excessive amounts of green tea could result in adverse side effects (whether hair fall is one of these effects is probably dependent on the person although I have never heard of anyone suffering from this).
In short, there may be extreme, extenuating circumstances when green tea can cause hair fall (<1% chance), but for the most part (99%), green tea does not cause hair fall.
Note: There may be cases where hair fall was caused by green tea that had gone bad/contaminated by other materials. It is best to purchase green tea from known brands and brew it yourself using.
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