When Rigoberto Alpizar visited his family in Rio Claro, Costa Rica, in July, he grew alarmed at his father's deteriorating heart condition. He took his father to see a doctor in San Jose; before returning home to the United States, says his brother Carlos, he taped little notes all over the house with a gentle reminder: "Please take your medication. I love you very much." But when it came to Alpizar's own condition—bipolar disorder—he apparently failed to heed that same advice, according to his wife's statements to authorities. Aboard a plane preparing to push away from the gate in Miami...