I'm sure that good professionals, therapists and hopefully police and legal people can tell the difference between liars and those telling the truth, although abusers are notoriously devious. Their lives revolve around lies and deceipt.
It's a choice between a rock and a hard place, but the truth usually comes out in the end.
I don't envy your decision, but be strong.
Go confidently in the direction of your dreams! Live the life you've imagined. As you simplify your life, the laws of the universe will be simpler.
Henry David Thoreau