How do you know for sure whether or not to use a closing? One good test is to ask yourself whether this email is more akin to an instant message/text or a business letter. If you're giving your teammate a quick update on an ongoing project, a formal closing might not be necessary; if you're throwing your hat in the ring for a promotion, it definitely is required. When all else fails, and you're still not sure, err on the side of caution and include it. You'll never go wrong by being too polite and respectful.
In a cover letter, keep your remarks brief. Your opening should explain what you are sending and why. In an optional second paragraph, you might include a summary of the information you are sending. A letter accompanying a proposal, for example, might point out sections in the proposal that might be of particular interest to the reader. The letter could then go on to present a key point or two explaining why the writer’s firm is the best one for the job. The closing paragraph should contain acknowledgements, offer additional assistance, or express the hope that the material will fulfill its purpose