Rescue -- A/An vs. The

Is it an East Lansing Fire Department incident report? Or the East Lansing Fire Department incident report.

In general, on first reference you'd be better off using an or a. That's because this report is certainly not the only incident report filed by East Lansing Fire Department. You are noting it's one among many reports on various incidents that the department handles every day.

Now, after establishing in the first reference you are referring to one report among many, then you are free to refer to it as the report.

Where you may vary in first references is when you are using a clearly distinct and one-of-a-kind document; e.g., according to the Declaration of Independence; according to the resignation letter from President Nixon, ect.

Otherwise, if it's a more common type of document, you may be better off with a or an in first reference.

Again, once you establish that, the should be acceptable in all subsequent references.