Well, in Los Angeles County, all this is outlined in Section 814 of the LA County EMT-I/Paramedic/MICN policy.
Basically, it outlines these obvious signs of death:
I. Determination of Death: A patient may be determined dead if, in addition to the absence of respiration, cardiac activity, and neurologic reflexes, one or more of the following physical or circumstantial conditions exist:
A. Decapitation
B. Massive crush injury
C. Penetrating or blunt injury with evisceration of the heart, lung or brain
D. Decomposition
E. Incineration
F. Pulseless, non-breathing victims with extrication time greater than fifteen minutes, where no resuscitative measures can be performed prior to extrication
G. Pulseless, non-breathing victims of a multiple victim incident where insufficient medical resources preclude initiating resuscitative measures
H. Drowning victims, when it is reasonably determined that submersion has been greater than one hour
I. Rigor Mortis (Requires assessment as described in section II.A.)
J. Post-Mortem Lividity (Requires assessment as described in section II.A.)
II. Patients Determined to be Dead:
A. If the initial assessment reveals rigor mortis and/or post-mortem lividity only,
EMT-Is and/or paramedics shall perform the following assessments to determine respiratory, cardiac, and neurologic status:
NOTE: Assessment steps may be performed concurrently.
1. Assessment of respiratory status:
a. Assure that the patient has an open airway.
b. Look, listen and feel for respirations. Auscultate the lungs for a minimum of 30 seconds.
2. Assessment of cardiac status:
a. Auscultate the apical pulse for a minimum of 60 seconds.
b. Adults and children: Palpate the carotid pulse for a minimum of 60 seconds.
Infants: Palpate the brachial pulse for a minimum of 60 seconds.
3. Assessment of neurological reflexes:
a. Check for pupil response with a penlight or flashlight.
b. Check for a response to painful stimuli.
I would assume that you have similar criteria in your area. Check your state's EMT Scope of Practice, and your local County's expanded Scope of Practice.
Also, be aware that your scope may change from time to time. I.E.: In LA County it is now recomended to poke all suspected fatilities with a pointed stick.
-Ian in LA