
One example of a believer, or at least a worshipper of God, committing suicide is in 2 Samuel 17:23 (KJV). "And when Ahithophel saw that his counsel was not followed, he saddled his ass, and arose, and gat him home to his house, to his city, and put his household in order, and hanged himself, and died, and was buried in the sepulchre of his father."

King Saul also killed himself but he had lost God's spirit long before that. The Bible says in 1 Samuel 31:3-4 (KJV), "And the battle went sore against Saul, and the archers hit him; and he was sore wounded of the archers. Then said Saul unto his armourbearer, 'Draw thy sword, and thrust me through therewith; lest these uncircumcised come and thrust me through, and abuse me.' But his armourbearer would not; for he was sore afraid. Therefore Saul took a sword, and fell upon it."

But God knows the heart. As he said in 1 Samuel 16:7 (KJV), "But the LORD said unto Samuel, 'Look not on his countenance, or on the height of his stature; because I have refused him: for the LORD seeth not as man seeth; for man looketh on the outward appearance, but the LORD looketh on the heart.'"
I'll be writing more about this in my next book called You Think You're Going to Heaven? There are some situations where we can't tell if somebody is in heaven or hell but God knows.