depression and play

A parent's depression is certainly going to have an impact on the child, because a depressed parent can't be fully responsive to their own needs or to their child's needs, and (often) can't reflect back their child's joy and liveliness. It's also confusing to the child, they miss their parent, who is not fully there, but they can't figure out how to miss them, because they are partly there. Also, people who are depressed are also often irritable and/or anxious. So depressed parents, like all depressed people, need to get good help--whether they feel like it or not (and they won't feel like it). The child needs someone to spend time with who can be lively and joyful with them, and someone who can help them process the confusing and maybe even scary feelings that come from having a depressed parent. They don't need this person full-time, but they do need it some of the time. (Don't ask me how much time, i don't know!)
If the depression is mild, a parent might be able to pull their attention out of the depression and onto the present time reality through play--just play anyway, set a timer so it doesn't feel too onerous, and get physical (fall over, run around, use a silly voice, you can even get an eeyore puppet and use an exaggerated depressed voice). Don't expect this to work if the depression is too severe.
Children who are living with a depressed parent in an ongoing way might or might not show it symbolically in their play or their behavior. Sometimes children wait until the difficulty is passed before they put it into their play.
Some things to look out for in a child are irritability, withdrawal, inability to self-soothe, anxious clinging.
If you have been depressed and are "back" to yourself, don't pretend with your child that it didn't happen. Bring it up. Introduce it as a theme in the play.
I want to be clear that I am talking about depression here, not grief. If you have lost a loved one and are grieving, play might be hard for a time, but your child needs to see your free flow of emotion and needs to see that flow from deep grief to ongoing processing of grief to a return to the world.