For a positive verb meaning "to do something about," we have "address" or "handle."
For a negative verb meaning leave alone or not do anything about or not give attention to, we have "neglect." Also "disregard" is a more neutral word, but it specifically means to not pay attention to rather than to omit action concerning.
Is there a verb without negative connotation that means "to omit action or activity concerning; to not do anything about"?
I am going to _____ this project, as I think the people running it are doing just fine on their own.
Edit: Since a couple people in the comments somehow think such a verb is intrinsically impossible—an interesting concept—I'll mention several other words that are similar in many ways and do not have any inherent negative connotation, at least demonstrating that it's not fundamentally impossible to have a word with the meaning I've described above, even if there isn't a well known word that does:
Words/idioms with similar meanings and without negative connotations include: abstain, refrain, leave alone, let be, hold off (on something), tolerate, live with.