diff --git a/.github/workflows/pythonapp.yml b/.github/workflows/pythonapp.yml
index aac0403ee..b0db1a7e1 100644
--- a/.github/workflows/pythonapp.yml
+++ b/.github/workflows/pythonapp.yml
@@ -153,6 +153,14 @@ jobs:
         run: pip install nanobind scikit-build-core[pyproject]
       - name: Install Basix
         run: pip install --no-build-isolation .
+      - name: Install mypy
+        run: pip install mypy
+      - name: Run mypy (module)
+        run: mypy -p basix
+      - name: Run mypy (test)
+        run: mypy test
+      # - name: Run mypy (demo)
+      #   run: mypy demo/python
 
   build-cmake:
     name: Build using C++ and Python parts separately and run tests
diff --git a/python/CMakeLists.txt b/python/CMakeLists.txt
index 8a946a2e3..54f5600d1 100644
--- a/python/CMakeLists.txt
+++ b/python/CMakeLists.txt
@@ -7,7 +7,7 @@ endif()
 
 project(basix_nanobind VERSION "0.9.0.0" LANGUAGES CXX)
 
-if (WIN32)
+if(WIN32)
     # Windows requires all symbols to be manually exported.
     # This flag exports all symbols automatically, as in Unix.
     set(CMAKE_WINDOWS_EXPORT_ALL_SYMBOLS TRUE)
@@ -112,15 +112,45 @@ else()
   set_target_properties(_basixcpp PROPERTIES INSTALL_RPATH ${_basix_dir})
 endif()
 
-install(TARGETS _basixcpp LIBRARY DESTINATION basix)
-
 # and the nanobind typing stubs.
-nanobind_add_stub(
-  _basixcpp_stub
-  MODULE basix._basixcpp
-  DEPENDS _basixcpp
-  VERBOSE
-  INSTALL_TIME
-  OUTPUT
-    basix/_basixcpp.pyi
-)
+if (WIN32)
+  # On Windows we cannot import basix._basixcpp without installing the package
+  # alongside its external dlls.
+
+  # This *must* be called prior to nanobind_add_stub
+  install(TARGETS _basixcpp LIBRARY DESTINATION basix)
+  # nanobind automatically installs into ${CMAKE_INSTALL_PREFIX} in
+  # INSTALL_TIME mode.
+  # DEPENDS is redundant in INSTALL_TIME mode - _basixcpp must be installed.
+  nanobind_add_stub(
+    _basixcpp_stub
+    MODULE basix._basixcpp
+    INSTALL_TIME
+    PATTERN_FILE ${CMAKE_CURRENT_SOURCE_DIR}/pattern_stub.txt
+    MARKER_FILE basix/py.typed
+    VERBOSE
+    OUTPUT
+      basix/_basixcpp.pyi
+  )
+else()
+  # On UNIX-like systems we can import the cpp compiled module before
+  # installing and rely on dynamic linking at import time.
+  nanobind_add_stub(
+    _basixcpp_stub
+    MODULE _basixcpp
+    PYTHON_PATH $<TARGET_FILE_DIR:_basixcpp>
+    DEPENDS _basixcpp
+    PATTERN_FILE ${CMAKE_CURRENT_SOURCE_DIR}/pattern_stub.txt
+    MARKER_FILE ${CMAKE_CURRENT_SOURCE_DIR}/basix/py.typed
+    VERBOSE
+    OUTPUT
+      _basixcpp.pyi
+  )
+
+  install(TARGETS _basixcpp LIBRARY DESTINATION basix)
+  install(FILES
+    ${CMAKE_CURRENT_SOURCE_DIR}/basix/py.typed
+    ${CMAKE_CURRENT_BINARY_DIR}/_basixcpp.pyi
+    DESTINATION basix
+  )
+endif()
diff --git a/python/basix/py.typed b/python/basix/py.typed
deleted file mode 100644
index e69de29bb..000000000
diff --git a/python/pattern_stub.txt b/python/pattern_stub.txt
index 24d5707f6..10c317831 100644
--- a/python/pattern_stub.txt
+++ b/python/pattern_stub.txt
@@ -1,2 +1,7 @@
-basix._basixcpp.tabulate_polynomial_set:
-    def tabulate_polynomial_set(celltype: CellType, polytype: PolysetType, d: int, n: int, x: Annotated[ArrayLike, dict(dtype='float64', writable=False, shape=(None, None), order='C')]) -> Annotated[ArrayLike, dict(dtype='float64', )]: ...
\ No newline at end of file
+tabulate_polynomial_set:
+    \from typing import TypeVar
+    \from numpy.typing import NDArray as _NDArray
+    \from numpy import float32 as _f32, float64 as _f64
+    _polynomial_set_floats = TypeVar("_polynomial_set_floats", _f32, _f64)
+
+    def tabulate_polynomial_set(celltype: CellType, polytype: PolysetType, d: int, n: int, x: _NDArray[_polynomial_set_floats],) -> _NDArray[_polynomial_set_floats]: ...