diff --git a/tests/python_package_test/test_dask.py b/tests/python_package_test/test_dask.py
index c9c075afb771..b3a982e0f23d 100644
--- a/tests/python_package_test/test_dask.py
+++ b/tests/python_package_test/test_dask.py
@@ -154,6 +154,7 @@ def test_classifier(output, centers, client, listen_port):
     dask_classifier = dask_classifier.fit(dX, dy, sample_weight=dw, client=client)
     p1 = dask_classifier.predict(dX)
     p1_proba = dask_classifier.predict_proba(dX).compute()
+    p1_local = dask_classifier.to_local().predict(X)
     s1 = _accuracy_score(dy, p1)
     p1 = p1.compute()
 
@@ -168,6 +169,8 @@ def test_classifier(output, centers, client, listen_port):
     assert_eq(y, p1)
     assert_eq(y, p2)
     assert_eq(p1_proba, p2_proba, atol=0.3)
+    assert_eq(p1_local, p2)
+    assert_eq(y, p1_local)
 
     client.close()
 
@@ -249,35 +252,6 @@ def test_training_does_not_fail_on_port_conflicts(client):
     client.close()
 
 
-def test_classifier_local_predict(client, listen_port):
-    X, y, w, dX, dy, dw = _create_data(
-        objective='classification',
-        output='array'
-    )
-
-    params = {
-        "n_estimators": 10,
-        "num_leaves": 10
-    }
-    dask_classifier = lgb.DaskLGBMClassifier(
-        time_out=5,
-        local_port=listen_port,
-        **params
-    )
-    dask_classifier = dask_classifier.fit(dX, dy, sample_weight=dw, client=client)
-    p1 = dask_classifier.to_local().predict(dX)
-
-    local_classifier = lgb.LGBMClassifier(**params)
-    local_classifier.fit(X, y, sample_weight=w)
-    p2 = local_classifier.predict(X)
-
-    assert_eq(p1, p2)
-    assert_eq(y, p1)
-    assert_eq(y, p2)
-
-    client.close()
-
-
 @pytest.mark.parametrize('output', data_output)
 def test_regressor(output, client, listen_port):
     X, y, w, dX, dy, dw = _create_data(
@@ -300,6 +274,8 @@ def test_regressor(output, client, listen_port):
     if output != 'dataframe':
         s1 = _r2_score(dy, p1)
     p1 = p1.compute()
+    p1_local = dask_regressor.to_local().predict(X)
+    s1_local = dask_regressor.to_local().score(X, y)
 
     local_regressor = lgb.LGBMRegressor(**params)
     local_regressor.fit(X, y, sample_weight=w)
@@ -309,10 +285,12 @@ def test_regressor(output, client, listen_port):
     # Scores should be the same
     if output != 'dataframe':
         assert_eq(s1, s2, atol=.01)
+        assert_eq(s1, s1_local, atol=.003)
 
     # Predictions should be roughly the same
     assert_eq(y, p1, rtol=1., atol=100.)
     assert_eq(y, p2, rtol=1., atol=50.)
+    assert_eq(p1, p1_local)
 
     client.close()
 
@@ -387,30 +365,6 @@ def test_regressor_quantile(output, client, listen_port, alpha):
     client.close()
 
 
-def test_regressor_local_predict(client, listen_port):
-    X, y, _, dX, dy, dw = _create_data('regression', output='array')
-
-    dask_regressor = lgb.DaskLGBMRegressor(
-        local_listen_port=listen_port,
-        random_state=42,
-        n_estimators=10,
-        num_leaves=10,
-        tree_type='data'
-    )
-    dask_regressor = dask_regressor.fit(dX, dy, sample_weight=dw, client=client)
-    p1 = dask_regressor.predict(dX)
-    p2 = dask_regressor.to_local().predict(X)
-    s1 = _r2_score(dy, p1)
-    p1 = p1.compute()
-    s2 = dask_regressor.to_local().score(X, y)
-
-    # Predictions and scores should be the same
-    assert_eq(p1, p2)
-    assert_eq(s1, s2)
-
-    client.close()
-
-
 @pytest.mark.parametrize('output', ['array', 'dataframe'])
 @pytest.mark.parametrize('group', [None, group_sizes])
 def test_ranker(output, client, listen_port, group):
@@ -437,6 +391,7 @@ def test_ranker(output, client, listen_port, group):
     dask_ranker = dask_ranker.fit(dX, dy, sample_weight=dw, group=dg, client=client)
     rnkvec_dask = dask_ranker.predict(dX)
     rnkvec_dask = rnkvec_dask.compute()
+    rnkvec_dask_local = dask_ranker.to_local().predict(X)
 
     local_ranker = lgb.LGBMRanker(**params)
     local_ranker.fit(X, y, sample_weight=w, group=g)
@@ -447,35 +402,7 @@ def test_ranker(output, client, listen_port, group):
     dcor = spearmanr(rnkvec_dask, y).correlation
     assert dcor > 0.6
     assert spearmanr(rnkvec_dask, rnkvec_local).correlation > 0.75
-
-    client.close()
-
-
-@pytest.mark.parametrize('output', ['array', 'dataframe'])
-@pytest.mark.parametrize('group', [None, group_sizes])
-def test_ranker_local_predict(output, client, listen_port, group):
-
-    X, y, w, g, dX, dy, dw, dg = _create_ranking_data(
-        output=output,
-        group=group
-    )
-
-    dask_ranker = lgb.DaskLGBMRanker(
-        time_out=5,
-        local_listen_port=listen_port,
-        tree_learner='data',
-        n_estimators=10,
-        num_leaves=10,
-        random_state=42,
-        min_child_samples=1
-    )
-    dask_ranker = dask_ranker.fit(dX, dy, group=dg, client=client)
-    rnkvec_dask = dask_ranker.predict(dX)
-    rnkvec_dask = rnkvec_dask.compute()
-    rnkvec_local = dask_ranker.to_local().predict(X)
-
-    # distributed and to-local scores should be the same.
-    assert_eq(rnkvec_dask, rnkvec_local)
+    assert_eq(rnkvec_dask, rnkvec_dask_local)
 
     client.close()