You check first, then ask the pro.

Don't think about "cost" as the first step. Landlord should pay for their property for long term return, right?

First check if there is any holes on the roof where animals can enter, then check all the opening to see if any vent net are missing. Then ask if the smell get worse, or better, if the AC fan is turned on. If true, check if any duct work has holes!

Finally, search around the attic to search for any dead meat.

If it is in the duct work--> find a plumber,

If it is in the Attic and you can see it --> animal control (pest are small bugs?)

Fix the hole afterwards.