I was not given a copy of the petition to be taken home. As such, I am hereby responding to allegations contained in the petition, relying solely on my memory as to its content.
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Change the last bit to, for example, "relying solely on what I remember."
It seems correct, but it sounds stiff and formal. "Legal" language tends to have a lot of extra words. It would make just as much sense to simply say "relying solely on my memory". It's obvious the "content" is what you're talking about. You could also replace "as such" with "so", etc.