Laboratory tests that should be obtained when a person is suspected or known to have cardiomegaly are: a complete blood count, thyroid stimulating hormone levels, and a blood urea nitrogen.  These are common, high yield tests. Other tests can be ordered based on suspicions as to the underlying cause of the cardiomegaly, obtained through patient history and physical examination.
Cardiomegaly laboratory findings
Cardiomegaly physical examination
Right heart failure laboratory findings
Pulmonary edema physical examination
Right heart failure physical examination
Constrictive pericarditis physical examination
Constrictive pericarditis laboratory findings
Cardiomegaly echocardiography or ultrasound