The probe centered on suspicions that the 2007 death of Kim's only child, Seo-yeon, may not be accidental, and her mother, Seo Hae-soon, might have let the 16-year-old die of pneumonia as she was the legal inheritor of her father's estate, including the copyrights to his music.
But police said they found no evidence backing such suspicions.
The case drew nationwide attention after a documentary film about the singer, produced by TV journalist Lee Sang-ho, raised such suspicions. Police began looking into the suspicions in September after Lee and a brother of the late singer filed complaints requesting an investigation.
Police questioned the widow three times and Kim's brother twice. Forty-seven others were also interviewed as witnesses, including the doctor who treated Kim's daughter as well as TV journalist Lee.
Officials said they determined there was no evidence that the widow intentionally neglected the daughter.
Police have confirmed that the daughter was diagnosed with a simple cold and experts have also told police that her condition could have deteriorated rapidly because she was suffering from a rare disease known as Kabuki syndrome.
Investigators also took into consideration the fact that an autopsy of her body at the time determined that she died of a lung disease and that no unusual elements other than cold medicine were found in her blood.
The outcome is in line with the investigation 10 years ago.
At that time, police also closed the daughter's case as accidental, based on the autopsy that concluded her death was caused by acute pneumonia, with no signs of external injuries.
Kim the musician committed suicide in 1996, when he was 32. His death sent shock waves through fans and the public, who loved his plaintive yet captivating vocals and sentimental lyrics that critics say portrayed individuals' sorrow and frustration at a time when the society was struggling in its early stage of democracy following rapid industrialization, source from the Yonhap.