Depression itself doesn't, you know, correlate 100% with self-harm. A person can be depressed. Most depressed people don't harm themselves. Most depressed people don't think of harming themselves. Seriously depressed people sometimes do.
Now, what we wanna differentiate in this, and I would encourage parents you get help in differentiating this, is a child telling you this because it works in terms of them getting attention or love from you, versus telling you this because they really are self-harming. And that's a subtle distinction sometimes because some children do find that it garners so much attention and so much compassion that it becomes functional for them as a way of getting love and getting support that might not otherwise be available. But a professional can help you sort that out.
