diff --git a/docs/release-notes/4031.fix.md b/docs/release-notes/4031.fix.md
new file mode 100644
index 0000000000..7bf2a2692a
--- /dev/null
+++ b/docs/release-notes/4031.fix.md
@@ -0,0 +1 @@
+{func}`scanpy.tl.umap` no longer silently mutates `adata.obsp['connectivities']` via a shared sparse buffer {smaller}`N Justice`
diff --git a/src/scanpy/tools/_umap.py b/src/scanpy/tools/_umap.py
index a1848173fa..74565595b2 100644
--- a/src/scanpy/tools/_umap.py
+++ b/src/scanpy/tools/_umap.py
@@ -216,7 +216,7 @@ def umap(  # noqa: PLR0913, PLR0915
         n_epochs = default_epochs if maxiter is None else maxiter
         x_umap, _ = simplicial_set_embedding(
             data=x,
-            graph=neighbors["connectivities"].tocoo(),
+            graph=neighbors["connectivities"].tocoo(copy=True),
             n_components=n_components,
             initial_alpha=alpha,
             a=a,
diff --git a/tests/test_embedding.py b/tests/test_embedding.py
index 692157a084..c99cbba8ea 100644
--- a/tests/test_embedding.py
+++ b/tests/test_embedding.py
@@ -75,6 +75,21 @@ def test_umap_init_paga(layout):
     sc.tl.umap(pbmc, init_pos="paga")
 
 
+def test_umap_preserves_connectivities():
+    # https://github.com/scverse/scanpy/issues/4028
+    pbmc = pbmc68k_reduced()[:100, :].copy()
+    conn = pbmc.obsp["connectivities"]
+    data_before = conn.data.copy()
+    nnz_before = conn.nnz
+
+    sc.tl.umap(pbmc)
+
+    assert_array_equal(data_before, conn.data)
+    assert conn.nnz == nnz_before
+    assert (conn.data == 0).sum() == 0, "CSR should have no explicit zeros"
+    assert "X_umap" in pbmc.obsm
+
+
 def test_diffmap():
     pbmc = pbmc68k_reduced()