The correct sentence is; There are no people in the park.
I believe the reason is because the word 'people' is plural (referring to more than one), so it takes the are form of the verb 'be'.
There is a man in the park. (one person)
There are 20 people in the park. (more than 1)
Or
You could say your sentence this way.....
There is nobody in the park. :roll:
As has been noted in this forum, all this can get confusing. For instance, consider the following:
There is/are a man and two women standing in the park.
(In such situations, avoid using "there" altogether.)
By the way, as Yogi Berra would say, nobody every goes to that park any more. It's too crowded.