Contacting HR directly regarding a job I am highly qualified for, but am not eligible due to the job being offered to current employees.

This is the second, possibly third, time I've seen this job posted for a local municipality. It is for a lead mechanic, but the position is only available for current employees of that municipality. I have recently moved to the area from across the country where I was a mechanic for a large municipality. The job posting has the contact info for the HR people handling hiring. Would I be out of line contacting these people with my resume and a letter stating a saw the posting and want to introduce myself and let them know I would be interested in working for them? (Did I just describe a cover letter?)

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