diff --git a/pyproject.toml b/pyproject.toml
index 3dcda98980..8244947a1e 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -166,6 +166,8 @@ check_untyped_defs = true
 disallow_untyped_decorators = true
 disallow_any_generics = true
 
+disallow_incomplete_defs = true
+
 [[tool.mypy.overrides]]
 module = [
     "zarr.v2._storage.store",
@@ -196,6 +198,13 @@ module = [
 ]
 disallow_any_generics = false
 
+[[tool.mypy.overrides]]
+module = [
+    "zarr.v2.*",
+    "zarr.array_v2",
+    "zarr.group"
+]
+disallow_incomplete_defs = false
 
 [tool.pytest.ini_options]
 doctest_optionflags = [
diff --git a/src/zarr/array.py b/src/zarr/array.py
index c1263230c0..18e26b64dd 100644
--- a/src/zarr/array.py
+++ b/src/zarr/array.py
@@ -39,7 +39,7 @@
 from zarr.sync import sync
 
 
-def parse_array_metadata(data: Any):
+def parse_array_metadata(data: Any) -> ArrayMetadata:
     if isinstance(data, ArrayMetadata):
         return data
     elif isinstance(data, dict):
@@ -192,7 +192,7 @@ def dtype(self) -> np.dtype:
     def attrs(self) -> dict:
         return self.metadata.attributes
 
-    async def getitem(self, selection: Selection):
+    async def getitem(self, selection: Selection) -> np.ndarray:
         assert isinstance(self.metadata.chunk_grid, RegularChunkGrid)
         indexer = BasicIndexer(
             selection,
@@ -231,7 +231,7 @@ async def _read_chunk(
         chunk_selection: SliceSelection,
         out_selection: SliceSelection,
         out: np.ndarray,
-    ):
+    ) -> None:
         chunk_spec = self.metadata.get_chunk_spec(chunk_coords)
         chunk_key_encoding = self.metadata.chunk_key_encoding
         chunk_key = chunk_key_encoding.encode_chunk_key(chunk_coords)
@@ -301,7 +301,7 @@ async def _write_chunk(
         chunk_coords: ChunkCoords,
         chunk_selection: SliceSelection,
         out_selection: SliceSelection,
-    ):
+    ) -> None:
         chunk_spec = self.metadata.get_chunk_spec(chunk_coords)
         chunk_key_encoding = self.metadata.chunk_key_encoding
         chunk_key = chunk_key_encoding.encode_chunk_key(chunk_coords)
@@ -350,7 +350,7 @@ async def _write_chunk(
 
     async def _write_chunk_to_store(
         self, store_path: StorePath, chunk_array: np.ndarray, chunk_spec: ArraySpec
-    ):
+    ) -> None:
         if np.all(chunk_array == self.metadata.fill_value):
             # chunks that only contain fill_value will be removed
             await store_path.delete()
@@ -514,7 +514,7 @@ def metadata(self) -> ArrayMetadata:
     def store_path(self) -> StorePath:
         return self._async_array.store_path
 
-    def __getitem__(self, selection: Selection):
+    def __getitem__(self, selection: Selection) -> np.ndarray:
         return sync(
             self._async_array.getitem(selection),
             self._async_array.runtime_configuration.asyncio_loop,
diff --git a/src/zarr/codecs/sharding.py b/src/zarr/codecs/sharding.py
index 948e46f132..d4f8b7dfc9 100644
--- a/src/zarr/codecs/sharding.py
+++ b/src/zarr/codecs/sharding.py
@@ -195,7 +195,7 @@ def create_empty(cls, chunks_per_shard: ChunkCoords) -> _ShardBuilder:
         obj.index = _ShardIndex.create_empty(chunks_per_shard)
         return obj
 
-    def append(self, chunk_coords: ChunkCoords, value: BytesLike):
+    def append(self, chunk_coords: ChunkCoords, value: BytesLike) -> None:
         chunk_start = len(self.buf)
         chunk_length = len(value)
         self.buf.extend(value)
@@ -424,7 +424,7 @@ async def _read_chunk(
         shard_spec: ArraySpec,
         runtime_configuration: RuntimeConfiguration,
         out: np.ndarray,
-    ):
+    ) -> None:
         chunk_spec = self._get_chunk_spec(shard_spec)
         chunk_bytes = shard_dict.get(chunk_coords, None)
         if chunk_bytes is not None:
diff --git a/src/zarr/indexing.py b/src/zarr/indexing.py
index 7c1a4df226..75bed63384 100644
--- a/src/zarr/indexing.py
+++ b/src/zarr/indexing.py
@@ -13,7 +13,7 @@ def _ensure_tuple(v: Selection) -> SliceSelection:
     return v
 
 
-def _err_too_many_indices(selection: SliceSelection, shape: ChunkCoords):
+def _err_too_many_indices(selection: SliceSelection, shape: ChunkCoords) -> None:
     raise IndexError(
         "too many indices for array; expected {}, got {}".format(len(shape), len(selection))
     )
@@ -23,7 +23,7 @@ def _err_negative_step():
     raise IndexError("only slices with step >= 1 are supported")
 
 
-def _check_selection_length(selection: SliceSelection, shape: ChunkCoords):
+def _check_selection_length(selection: SliceSelection, shape: ChunkCoords) -> None:
     if len(selection) > len(shape):
         _err_too_many_indices(selection, shape)
 
@@ -179,7 +179,7 @@ def c_order_iter(chunks_per_shard: ChunkCoords) -> Iterator[ChunkCoords]:
     return itertools.product(*(range(x) for x in chunks_per_shard))
 
 
-def is_total_slice(item: Selection, shape: ChunkCoords):
+def is_total_slice(item: Selection, shape: ChunkCoords) -> bool:
     """Determine whether `item` specifies a complete slice of array with the
     given `shape`. Used to optimize __setitem__ operations on the Chunk
     class."""
diff --git a/src/zarr/store/local.py b/src/zarr/store/local.py
index 1e9e880875..73e3c6c0e1 100644
--- a/src/zarr/store/local.py
+++ b/src/zarr/store/local.py
@@ -34,13 +34,14 @@ def _put(
     value: BytesLike,
     start: Optional[int] = None,
     auto_mkdir: bool = True,
-):
+) -> int | None:
     if auto_mkdir:
         path.parent.mkdir(parents=True, exist_ok=True)
     if start is not None:
         with path.open("r+b") as f:
             f.seek(start)
             f.write(value)
+        return None
     else:
         return path.write_bytes(value)