I guess I haven't tackled this one yet! I don't think there's a hard and fast rule for query letter format, but I would write something like:
Dear Ms. Jones,
My writing partner and I are seeking representation. We have written a pilot called MARCHING BANDITS, a GLEE-meets-21 JUMP STREET comedy about fugitive criminals who take cover as high school band members. If you would be interested in reading it, you can reach us at (310) 555-9874 or firstname.lastname@example.org .
We look forward to hearing from you!
Meredith Smith and Jane Smith
Make sure the tone and genre of your script are clear. If the script has won a contest, you can also include that - but unless it's a prestigious contest like The Nicholl Fellowship, agents won't care very much. The agent I used to work for would say, "anyone can win a contest," and having done some reading for contests, I can vouch for the poor quality of contest submissions.
You might also consider writing "I graduated from USC with an MFA in Screenwriting" if that's true - but again, that won't necessarily impress people. As an assistant reading query letters, I remember thinking "didn't they teach you at USC that very few writers get representation from query letters?" Use your judgment about whether you think your school sounds impressive. Most don't.
Remember that your query letter will go to an assistant, not the actual agent. Don't do anything to bore the assistant or annoy the assistant and make him/her recycle the letter immediately. I used to get really annoyed when people would ramble on and on about their lives. I don't care that you're a butter sculptor from Tarzana! I have shit to do! If you write comedy, you can try to be funny (and I hope your logline sounds funny)...but don't go on and on. Avoid jokes altogether if you are not funny.
Also remember that most big agencies have policies requiring assistants to send query letters straight to business affairs, where another assistant will generate a letter telling you that the agency does not accept unsolicited material. Even if you manage to avoid this (very occasionally, some people ARE looking for new material), you will probably get thrown into the recycling bin. Please read all my other posts on query letters to understand why querying is largely ineffective.
In your email you said you've finished one script. Keep writing! You may not be ready for representation.