Can a paremedic determine a time of death?

That's possible, but unlikely. The medical examiner's office is charged with determining the cause and time of death:

Determining the Time of Death

The time of death can, with variable accuracy, be estimated by determining:

1. the temperature of the body and the rate of cooling;

2. the degree of postmortem lividity (hypostasis);

3. the degree of rigor mortis;

4. putrefaction;

5. insect activity; and,

6. analyzing stomach contents

http://www.relentlessdefense.com/autopsy.html