Polymerase Chain reaction (PCR) is a key tool to diagnose Covid-19. Yet access to PCR is often limited. In this paper, we develop a clinical strategy for prescribing PCR to patients based on data from COVIDOM, a French cohort of 54,000 patients with clinically suspected Covid-19 including 12,810 patients tested by PCR. Using a machine learning algorithm (a decision tree), we show that symptoms alone are sufficient to predict PCR outcome with a mean average precision of 86%. We identify combinations of symptoms that are predictive of PCR positivity (90% for anosmia/ageusia) or negativity (only 30% of PCR+ for a subgroup with cardiopulmonary symptoms): in both cases, PCR provides little added diagnostic value. We deduce a prescribing strategy based on clinical presentation that can improve the global efficiency of PCR testing.