diff --git a/jedi/api/helpers.py b/jedi/api/helpers.py
index 5f51d098..c95ea2dd 100644
--- a/jedi/api/helpers.py
+++ b/jedi/api/helpers.py
@@ -252,7 +252,10 @@ def get_call_signature_details(module, position):
     leaf = module.get_leaf_for_position(position, include_prefixes=True)
     if leaf.start_pos >= position:
         # Whitespace / comments after the leaf count towards the previous leaf.
-        leaf = leaf.get_previous_leaf()
+        try:
+            leaf = leaf.get_previous_leaf()
+        except IndexError:
+            return None
 
     if leaf == ')':
         if leaf.end_pos == position:
diff --git a/test/test_api/test_call_signatures.py b/test/test_api/test_call_signatures.py
index 5d09cdc9..9cba90f1 100644
--- a/test/test_api/test_call_signatures.py
+++ b/test/test_api/test_call_signatures.py
@@ -285,6 +285,7 @@ def test_no_signature():
     X()(""")
     assert Script(s).call_signatures() == []
     assert len(Script(s, column=2).call_signatures()) == 1
+    assert Script('').call_signatures() == []
 
 
 def test_dict_literal_in_incomplete_call():