Do you put a period at the end of a poem?

Unless there is a specific style of poetry that one is attempting to emulate, poetry is free of any restrictions of grammar and punctuation.

However, the decision to use or not use any form of punctuation or grammar in a poem must be purposeful and not just an error. e e Cummings in particular purposefully eschews the use of punctuation or even capitalisation (hence how his name has been spelt here) despite being a traditional poet who often used a Sonnet style.

e e Cummings' use or misuse or lack of grammatical rules draws attention to the content of the poem, the reader drawing the rhythm and meter of the poem from purely syntactic clues.

To take this even further, there is no real requirement to put the Words in order, on separate lines, with spaces between them or with structure at all, if that was relevant to the meaning you wished to convey.

Consider:

"She walks in beauty, like the night

Of cloudless climes and starry skies;

And all that's best of dark and bright

Meet in her aspect and her eyes:"

--Lord Byron

Compared to:

"She walks

in b e a u t y like the n i g h t

of

cloudless climes

and starry skies;

And all that's best of

dark

and

B R I G H T

Meet in her aspect

a

n

d

her

eyes."

--Lord Byron

Of course it ruins it but that style might be more suitable for a moment with drama and tempest than the gushing love songs of Byron.

Experiment. You can't be wrong, but you can be careless or boring.