diff --git a/src/cmd/gofmt/gofmt_test.go b/src/cmd/gofmt/gofmt_test.go
index 903ba2177d..e4d5796f3c 100644
--- a/src/cmd/gofmt/gofmt_test.go
+++ b/src/cmd/gofmt/gofmt_test.go
@@ -81,6 +81,7 @@ var tests = []struct {
 	{"testdata/stdin*.input", "-stdin"},
 	{"testdata/comments.input", ""},
 	{"testdata/import.input", ""},
+	{"testdata/crlf.input", ""}, // test case for issue 3961; see also TestCRLF
 }
 
 func TestRewrite(t *testing.T) {
@@ -103,3 +104,24 @@ func TestRewrite(t *testing.T) {
 		}
 	}
 }
+
+func TestCRLF(t *testing.T) {
+	const input = "testdata/crlf.input"   // must contain CR/LF's
+	const golden = "testdata/crlf.golden" // must not contain any CR's
+
+	data, err := ioutil.ReadFile(input)
+	if err != nil {
+		t.Error(err)
+	}
+	if bytes.Index(data, []byte("\r\n")) < 0 {
+		t.Errorf("%s contains no CR/LF's", input)
+	}
+
+	data, err = ioutil.ReadFile(golden)
+	if err != nil {
+		t.Error(err)
+	}
+	if bytes.Index(data, []byte("\r")) >= 0 {
+		t.Errorf("%s contains CR's", golden)
+	}
+}
diff --git a/src/cmd/gofmt/testdata/crlf.golden b/src/cmd/gofmt/testdata/crlf.golden
new file mode 100644
index 0000000000..57679f770f
--- /dev/null
+++ b/src/cmd/gofmt/testdata/crlf.golden
@@ -0,0 +1,12 @@
+/*
+	Source containing CR/LF line endings.
+	The gofmt'ed output must only have LF
+	line endings.
+*/
+package main
+
+func main() {
+	// line comment
+	println("hello, world!") // another line comment
+	println()
+}
diff --git a/src/cmd/gofmt/testdata/crlf.input b/src/cmd/gofmt/testdata/crlf.input
new file mode 100755
index 0000000000..61a1aa0b4e
--- /dev/null
+++ b/src/cmd/gofmt/testdata/crlf.input
@@ -0,0 +1,12 @@
+/*
+	Source containing CR/LF line endings.
+	The gofmt'ed output must only have LF
+	line endings.
+*/
+package main
+
+func main() {
+	// line comment
+	println("hello, world!") // another line comment
+	println()
+}