1. This story is written by Mary.
2. This story was written by Mary.
Which is correct and natural?
Both are fine. The story exists in the present, so you can use the present tense if you want. Mary wrote the story in the past, so you can use the past tense if you want.
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Both are fine.
The story exists in the present, so you can use the present tense if you want.
Mary wrote the story in the past, so you can use the past tense if you want.
CJ