Baptist Health Medical Center-Little Rock (501) 202-1914 phone (501) 202-1555 fax. Baptist Health Rehabilitation Institute (501) 202-1914 phone (501) 202-1555 fax . Baptist Health Medical Center-North Little Rock (501) 202-3081 phone (501) 202-3079 fax. Baptist Health Medical Center-Conway (501) 585-2016 phone (501) 585-2922 fax. Baptist Health-Fort Smith: (479) 441-4050 phone (479) 441-3779 fax.