diff --git a/pandas/tests/extension/base/reshaping.py b/pandas/tests/extension/base/reshaping.py
index 89c9ed3674a66..ec21898852888 100644
--- a/pandas/tests/extension/base/reshaping.py
+++ b/pandas/tests/extension/base/reshaping.py
@@ -94,6 +94,19 @@ def test_concat_columns(self, data, na_value):
         result = pd.concat([df1["A"], df2["B"]], axis=1)
         self.assert_frame_equal(result, expected)
 
+    def test_concat_extension_arrays_copy_false(self, data, na_value):
+        # GH 20756
+        df1 = pd.DataFrame({"A": data[:3]})
+        df2 = pd.DataFrame({"B": data[3:7]})
+        expected = pd.DataFrame(
+            {
+                "A": data._from_sequence(list(data[:3]) + [na_value], dtype=data.dtype),
+                "B": data[3:7],
+            }
+        )
+        result = pd.concat([df1, df2], axis=1, copy=False)
+        self.assert_frame_equal(result, expected)
+
     def test_align(self, data, na_value):
         a = data[:3]
         b = data[2:5]
diff --git a/pandas/tests/extension/test_sparse.py b/pandas/tests/extension/test_sparse.py
index 6ebe71e173ec2..854bb8adcb100 100644
--- a/pandas/tests/extension/test_sparse.py
+++ b/pandas/tests/extension/test_sparse.py
@@ -132,6 +132,10 @@ def test_concat_columns(self, data, na_value):
         self._check_unsupported(data)
         super().test_concat_columns(data, na_value)
 
+    def test_concat_extension_arrays_copy_false(self, data, na_value):
+        self._check_unsupported(data)
+        super().test_concat_extension_arrays_copy_false(data, na_value)
+
     def test_align(self, data, na_value):
         self._check_unsupported(data)
         super().test_align(data, na_value)