diff --git a/labelme/shape.py b/labelme/shape.py
index 50d73fc0e..609e9b68e 100644
--- a/labelme/shape.py
+++ b/labelme/shape.py
@@ -325,6 +325,10 @@ def nearestEdge(self, point, epsilon):
     def containsPoint(self, point) -> bool:
         if self.shape_type in ["line", "linestrip", "points"]:
             return False
+        if self.shape_type == "point":
+            if not self.points:
+                return False
+            return labelme.utils.distance(point - self.points[0]) <= self.point_size / 2
         if self.mask is not None:
             raw_y = int(round(point.y() - self.points[0].y()))
             raw_x = int(round(point.x() - self.points[0].x()))
diff --git a/tests/unit/shape_contains_point_test.py b/tests/unit/shape_contains_point_test.py
new file mode 100644
index 000000000..5e9e518d4
--- /dev/null
+++ b/tests/unit/shape_contains_point_test.py
@@ -0,0 +1,45 @@
+from __future__ import annotations
+
+from PyQt5 import QtCore
+
+from labelme.shape import Shape
+
+
+def _make_point_shape(x: float, y: float) -> Shape:
+    """Create a point shape with a single point at (x, y)."""
+    shape = Shape(shape_type="point")
+    shape.addPoint(QtCore.QPointF(x, y))
+    return shape
+
+
+def test_point_shape_contains_center():
+    """Clicking exactly on a point shape should return True."""
+    shape = _make_point_shape(100.0, 200.0)
+    assert shape.containsPoint(QtCore.QPointF(100.0, 200.0)) is True
+
+
+def test_point_shape_contains_within_radius():
+    """Clicking within point_size/2 of the center should return True."""
+    shape = _make_point_shape(100.0, 200.0)
+    # point_size defaults to 8, so radius = 4. A point 3px away should hit.
+    assert shape.containsPoint(QtCore.QPointF(103.0, 200.0)) is True
+
+
+def test_point_shape_at_exact_boundary():
+    """Clicking exactly at point_size/2 distance should return True (inclusive)."""
+    shape = _make_point_shape(100.0, 200.0)
+    # point_size defaults to 8, so radius = 4. Exactly 4px away should hit.
+    assert shape.containsPoint(QtCore.QPointF(104.0, 200.0)) is True
+
+
+def test_point_shape_outside_radius():
+    """Clicking more than point_size/2 away should return False."""
+    shape = _make_point_shape(100.0, 200.0)
+    # 10px away, well outside the radius of 4
+    assert shape.containsPoint(QtCore.QPointF(110.0, 200.0)) is False
+
+
+def test_point_shape_empty_points():
+    """A point shape with no points should return False, not raise."""
+    shape = Shape(shape_type="point")
+    assert shape.containsPoint(QtCore.QPointF(0.0, 0.0)) is False