The simple answer is, "it depends." Some fireplace ashes are toxic and others are not. It all depends on what was burned in the fireplace. If you burned treated wood, such as pressure-treated lumber, then the ashes will be toxic because of the chemicals used to treat the wood. If you burned untreated wood, then the ashes are typically safe to use in the garden.
If you're not sure what type of wood was burned, it is usually better to be on the safe side and avoid using them for gardening. It's a simple matter of avoiding potential problems that could occur if treated lumber was used instead of untreated lumber. If you do have some ash that you're not sure about, it's always a good idea to test them in an inconspicuous spot before using them anywhere else.
If the ashes are from a gas fireplace, they will be safe to use in the garden. However, if you have an wood-burning fireplace, you'll need to wait until the ashes have completely cooled before using them. The proper way to test the ashes is by adding some water to a small amount of the ash in a bowl or jar, and then stir it with your finger and see if it feels gritty. If you can still feel grit on your fingers after stirring, then they're probably not ready for use yet.
