After restoring a radio and contacting DiMA, she is led to believe that she is a synth; this is reinforced by her inexplicable dreams about waking up in a lab and innate mechanical ability, although she does have her own doubts as to if this is the truth, nor can she prove it.
She is curious and empathetic, as shown by her pursuit of DiMA's radio signal and her desire to help the people of Acadia. When she was living with her parents, she was frequently bored, as she was isolated from the wasteland in her remote home. Her grandfather's passing worsened this feeling of boredom.
There is no evidence to support Kasumi's belief she is a synth, beyond her own feelings. Going to the Railroad or the Institute can lead the player to have conversations with Boxer or Dr. William Moseley, respectively, about whether Kasumi is human or synth, but neither conversation confirms or denies Kasumi's belief.
If Acadia is destroyed and Kasumi is killed she will not drop a synth component. Some synths, like Glory and Roger Warwick, do not drop a synth component when they die.
Even if Kasumi is "reclaimed" with the synths of Acadia for the Institute by informing Dr. Moseley about Acadia for Forbidden Knowledge, the player is never told whether she was human or synth.
Should Acadia (and Kasumi) be reported to the Institute, Dr. William Moseley will indicate that they have no record of any synth deployment with that identity, meaning she cannot be a synth under Institute control. He does, however, raise the possibility her personality may have been given after a memory wipe.
↑Sole Survivor: "Do you have any proof that you're actually a synth?" Kasumi Nakano: "Little things. Dreams of waking up in a lab. Years I can't remember from when I was a kid. Not to mention how I never quite fit in back at home..." (Kasumi Nakano's dialogue)
↑Sole Survivor: "I know it must be hard for you. I just want to make sure you're here for the right reasons." Kasumi Nakano: "Yeah, so am I... I mean... yes, I believe I'm a synth, but... there's something wrong here. With Acadia. There's more going on than just the refuge. I can't leave until I've gotten to the bottom of it. I've done enough running..." (Kasumi Nakano's dialogue)
↑Kenji Nakano: "Kasumi... Is it true? You're not my daughter?" Kasumi Nakano: "I... Yes it's true... I mean... I can't prove it, but when I made it to Acadia, I just knew..." Kenji Nakano: "Where's the real Kasumi?" Kasumi Nakano: "I don't know. There's no telling when I replaced her. I... I never knew what I was before. I never wanted to hurt you..." (Kenji Nakano and Kasumi Nakano's dialogue