diff --git a/flang/lib/Optimizer/Builder/FIRBuilder.cpp b/flang/lib/Optimizer/Builder/FIRBuilder.cpp
--- a/flang/lib/Optimizer/Builder/FIRBuilder.cpp
+++ b/flang/lib/Optimizer/Builder/FIRBuilder.cpp
@@ -1157,8 +1157,18 @@
     if (fir::isa_ref_type(rhsVal.getType()))
       rhsVal = builder.create<fir::LoadOp>(loc, rhsVal);
     mlir::Value lhsAddr = fir::getBase(lhs);
-    rhsVal = builder.createConvert(loc, fir::unwrapRefType(lhsAddr.getType()),
-                                   rhsVal);
+    mlir::Type lhsTargetType = fir::unwrapRefType(lhsAddr.getType());
+    mlir::Type rhsTy = rhsVal.getType();
+    if (rhsTy != lhsTargetType) {
+      if (fir::ConvertOp::canBeConverted(rhsTy, lhsTargetType))
+        rhsVal = builder.createConvert(
+            loc, fir::unwrapRefType(lhsAddr.getType()), rhsVal);
+      else
+        // we can't convert rhs to match lhs, so instead convert lhs e.g.
+        // convert !fir.ref<A> to !fir.ref<B>
+        lhsAddr =
+            builder.createConvert(loc, ReferenceType::get(rhsTy), lhsAddr);
+    }
     builder.create<fir::StoreOp>(loc, rhsVal, lhsAddr);
   }
 }
diff --git a/flang/test/HLFIR/assign-codegen.fir b/flang/test/HLFIR/assign-codegen.fir
--- a/flang/test/HLFIR/assign-codegen.fir
+++ b/flang/test/HLFIR/assign-codegen.fir
@@ -267,3 +267,26 @@
 // CHECK:           %[[VAL_13:.*]] = fir.call @_FortranAAssign(%[[VAL_10]], %[[VAL_11]], %[[VAL_12]], %{{.*}}) : (!fir.ref<!fir.box<none>>, !fir.box<none>, !fir.ref<i8>, i32) -> none
 // CHECK:           return
 // CHECK:         }
+
+// Test we can assign types which cannot be converted e.g. logical -> complex
+func.func @_QPe1() -> !fir.logical<4> {
+  %0 = fir.alloca !fir.complex<4> {bindc_name = "f1", uniq_name = "_QFf1Ef1"}
+  %1:2 = hlfir.declare %0 {uniq_name = "_QFf1Ef1"} : (!fir.ref<!fir.complex<4>>) -> (!fir.ref<!fir.complex<4>>, !fir.ref<!fir.complex<4>>)
+  %2:2 = hlfir.declare %1#1 {uniq_name = "_QFf1Ee1"} : (!fir.ref<!fir.complex<4>>) -> (!fir.ref<!fir.complex<4>>, !fir.ref<!fir.complex<4>>)
+  %false = arith.constant false
+  %3 = fir.convert %false : (i1) -> !fir.logical<4>
+  // this is the important bit:
+  hlfir.assign %3 to %2#0 : !fir.logical<4>, !fir.ref<!fir.complex<4>>
+  %4 = fir.convert %2#1 : (!fir.ref<!fir.complex<4>>) -> !fir.ref<!fir.logical<4>>
+  %5 = fir.load %4 : !fir.ref<!fir.logical<4>>
+  return %5 : !fir.logical<4>
+}
+// CHECK-LABEL: func.func @_QPe1()
+// CHECK-NEXT:    %[[F1_ALLOC:.*]] = fir.alloca !fir.complex<4>
+// CHECK-NEXT:    %[[F1_DECL:.*]] = fir.declare %[[F1_ALLOC]]
+// CHECK-NEXT:    %[[E1_DECL:.*]] = fir.declare %[[F1_DECL]]
+// CHECK-NEXT:    %[[FALSE:.*]] = arith.constant false
+// CHECK-NEXT:    %[[FALSE_LOGICAL:.*]] = fir.convert %[[FALSE]]
+// this is the important bit:
+// CHECK-NEXT:    %[[CONV:.*]] = fir.convert %[[E1_DECL]] : (!fir.ref<!fir.complex<4>>) -> !fir.ref<!fir.logical<4>>
+// CHECK-NEXT:    fir.store %[[FALSE_LOGICAL]] to %[[CONV]]