Should thrombolytic therapy be given to a patient in cardiac arrest secondary to presumed myocardial infarction?

No, with reservations.

A recent study in the New England Journal of Medicine evaluated this question. They found no difference between placebo and tenecteplase for the primary end point of 30 day survival or the secondary end points of hospital admission, return of spontaneous circulation, 24 hour survival, survival to hospital discharge or neurologic outcome.

Despite this, in a young 40 year old with no other options and a limited down time I might still consider giving it a try.

Bottiger, B. MD et al. "Thromboysis during Resuscitation for Out-of-Hospital Cardiac Arrest" N Engl J Med 2008; 359: 2651-62