Very often a question will have more close votes than downvotes. When those with enough (3,000) reputation cast a close vote on a question, is it also worthwhile they downvote? (In fact, this also applies to people with any rep score who flag questions for review.)
The cast close vote description says:
When should I close a question?
Questions that are sufficiently off-topic, as outlined in the FAQ, should be closed by casting close votes. Questions that are sufficiently similar to older questions should be closed by casting close votes.
The vote down description says:
When should I vote down?
Use your downvotes whenever you encounter an egregiously sloppy, no-effort-expended post, or an answer that is clearly and perhaps dangerously incorrect.
The downvote tooltip says:
This question does not show any research effort; it is unclear or not useful
Down voting questions doesn't cost you anything. If you think a question is bad enough to be to closed, does it also deserve a downvote too?
For example, a question asks for the definition of a word should be voted to be closed as general reference. It shows no research so gets a downvote.
Finally, the negative vote tally will sends a clear message for others to check if they should vote to close, and also to all other users to help them judge what makes a good question.
Or are there better reasons not to downvote when voting to close?