Hi Lynn,
No need for a medical report. But you do need a criminal report and a letter proving your income. In the pensionado residency that would be Social Security or a pension bringing in $1,000 a month. In rentista residency that would be non-job income from investments, CDs, retirement account, etc. that bring in $2,500 a month or a deposit of $60,000 in a Costa Rican bank.
You can review requirements and paper work necessary at the U.S. Embassy website here: http://costarica.usembassy.gov/cr-residency.html