This is the biggest debate in the Fallout community. If you play through her story in a repack or the retail version, the evidence is surprisingly thin on both sides:
: She has vivid "dreams" of waking up in a lab, and some unique Synths (like Glory) also don't drop components upon death. How to Save Kasumi Nakano
: Speak to Kasumi after the main conflict is resolved and use a Charisma check to convince her that her family loves her, regardless of whether she is a human or a Synth.
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: Broker a peace deal between the three factions or destroy the threats to Acadia without harming the Synths.
: Complete DiMA's memory puzzles to uncover the truth about his past.
: If Kasumi dies during the game, she does not drop a Synth Component . Furthermore, the Institute has no record of her being one of their units.