diff --git a/fsspec/implementations/local.py b/fsspec/implementations/local.py
index 17f96c1b8..a6fa7691d 100644
--- a/fsspec/implementations/local.py
+++ b/fsspec/implementations/local.py
@@ -122,6 +122,7 @@ def cp_file(self, path1, path2, **kwargs):
             self.makedirs(self._parent(path2), exist_ok=True)
         if self.isfile(path1):
             shutil.copyfile(path1, path2)
+            shutil.copystat(path1, path2)
         elif self.isdir(path1):
             self.mkdirs(path2, exist_ok=True)
         else: