Initially, you may think greeting styles are not that significant, but as mentioned previously, first impressions make a huge difference in the overall picture being chosen by the hiring committee.
Therefore, it is important to research who your audience could be when reading. Will it be addressed to an entire committee, to one individual, or to a general department? It is for you to find out and decide what greeting may best suit the position at hand and the reader whose hand it falls into. However, it is highly suggested that you research exactly who will read this cover letter initially and address them specifically. This shows initiative on your part; that you are willing to take that extra step to give it a personal touch and show them that you are a go-getter.
For example, if the chairperson of the hiring committee's name is Mr. Christopher Johnson, it may be beneficial to use his name in the greeting of your letter (i.e. Dear Mr. Johnson). However, if it is not specified, then you can simply address it as To Whom It May Concern. You can also try contacting the district's personnel office and ask for the person's name in charge of the hiring committee.
Note: Please keep in mind that this is a professional business letter, so the department or chairperson's name (if applicable) and school district's full address should be listed in the top left corner. Your name/address should be included either to the left as well or to the right above the recipient's information.
In addition, check for use of proper grammar and make sure there are no typos, including proper spellings of names. How embarrassing would it be to spell the chairperson's name wrong that may hire you for a job?