Mr White, 64, was reported missing last Tuesday and found dead at the Christian ministry's headquarters in Oklahoma the following day.
On the day he disappeared, police in Bartlesville received a report that Mr White had molested a 10-year-old girl.
Employees found a letter in his vehcile indicating that he was "suicidal or possibly fleeing to avoid investigation", which was given to police.
"You can take it either way," said Bartlesville Police Captain Jay Hastings. "It was kind of a goodbye letter. You don't know if he was talking about himself."
Voice of the Martyrs, which supports persecuted Christians worldwide, said in a statement that no one in the organisation's leadership or Board of Directors was aware of the allegations at the time of Mr White's death.
"Rather than face those allegations, and all of the resulting fallout for his family and this ministry and himself, Tom appears to have chosen to take his own life," VOM said in a statement.
"There is no doubt that Tom cared about his wife, his children and his grandchildren. And there's no doubt that he cared about VOM."
"We are deeply saddened by these events. Our hearts are broken.
"However, the work that God has called VOM to do is bigger than any one of us. There are persecuted Christians who need our help. The legal process will go forward, and we will continue serving with our persecuted brothers and sisters.
"We appreciate the many who are praying for our work, and we encourage you to join us in praying for Tom's family during this difficult time, as well as the family of the alleged victim."
Mr White served with Voice of the Martyrs for more than 30 years. According to a notice on the organisation's website, VOM president James E Dau will issue a statement later this week.