Punctuation in poetry is optional since poetry breaks the rules. In my poems, I often use punctuation, but there are a few poems where I don't. It's up to you as the poet to decide what will work best for your poem.
A way that might help you determine whether your poem is better with or without punctuation is by reading it out loud. Take a close look at the pacing of your poem when you do this. Are there too many interruptions with punctuation? If so, this could make your poem sound choppy and slow. I recommend writing two versions of your poem--one with punctuation and one without to see which one you like the best.
My poem when mermaids sing doesn't have much punctuation. You'll find the first stanza of that poem below.
Example: "a warm purple glow
two lily petals
part the glimmering
darkness"
Now, let's look at an early draft of this same stanza when I used punctuation.
Example: "a warm, purple glow,
two lily petals
part the glimmering
darkness."
In this example, the punctuation makes the poem feel too choppy, especially since I wrote the poem with very short lines. My critique group suggested I remove the punctuation to help the poem flow better.
