diff --git a/pgtype_test.go b/pgtype_test.go
index 8771b77f..9602f419 100644
--- a/pgtype_test.go
+++ b/pgtype_test.go
@@ -1,6 +1,7 @@
 package pgtype_test
 
 import (
+	"bytes"
 	"net"
 	"testing"
 
@@ -9,6 +10,8 @@ import (
 	_ "github.com/jackc/pgx/v4/stdlib"
 	_ "github.com/lib/pq"
 	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+	errors "golang.org/x/xerrors"
 )
 
 // Test for renamed types
@@ -41,7 +44,7 @@ func mustParseMacaddr(t testing.TB, s string) net.HardwareAddr {
 	return addr
 }
 
-func TestConnInfoScanUnknownOID(t *testing.T) {
+func TestConnInfoScanUnknownOIDToStringsAndBytes(t *testing.T) {
 	unknownOID := uint32(999999)
 	srcBuf := []byte("foo")
 	ci := pgtype.NewConnInfo()
@@ -74,3 +77,53 @@ func TestConnInfoScanUnknownOID(t *testing.T) {
 	assert.NoError(t, err)
 	assert.Equal(t, []byte("foo"), []byte(rb))
 }
+
+type pgCustomType struct {
+	a string
+	b string
+}
+
+func (ct *pgCustomType) DecodeText(ci *pgtype.ConnInfo, buf []byte) error {
+	// This is not a complete parser for the text format of composite types. This is just for test purposes.
+	if buf == nil {
+		return errors.New("cannot parse null")
+	}
+
+	if len(buf) < 2 {
+		return errors.New("invalid text format")
+	}
+
+	parts := bytes.Split(buf[1:len(buf)-1], []byte(","))
+	if len(parts) != 2 {
+		return errors.New("wrong number of parts")
+	}
+
+	ct.a = string(parts[0])
+	ct.b = string(parts[1])
+
+	return nil
+}
+
+func TestConnInfoScanUnknownOIDToCustomType(t *testing.T) {
+	unknownOID := uint32(999999)
+	ci := pgtype.NewConnInfo()
+
+	var ct pgCustomType
+	err := ci.Scan(unknownOID, pgx.TextFormatCode, []byte("(foo,bar)"), &ct)
+	assert.NoError(t, err)
+	assert.Equal(t, "foo", ct.a)
+	assert.Equal(t, "bar", ct.b)
+
+	// Scan value into pointer to custom type
+	var pCt *pgCustomType
+	err = ci.Scan(unknownOID, pgx.TextFormatCode, []byte("(foo,bar)"), &pCt)
+	assert.NoError(t, err)
+	require.NotNil(t, pCt)
+	assert.Equal(t, "foo", pCt.a)
+	assert.Equal(t, "bar", pCt.b)
+
+	// Scan null into pointer to custom type
+	err = ci.Scan(unknownOID, pgx.TextFormatCode, nil, &pCt)
+	assert.NoError(t, err)
+	assert.Nil(t, pCt)
+}