diff --git a/snowflake/datadog_checks/snowflake/check.py b/snowflake/datadog_checks/snowflake/check.py
index b5e548b95ccdd..f33c6634268f0 100644
--- a/snowflake/datadog_checks/snowflake/check.py
+++ b/snowflake/datadog_checks/snowflake/check.py
@@ -32,7 +32,7 @@ class SnowflakeCheck(AgentCheck):
 
     __NAMESPACE__ = 'snowflake'
 
-    SERVICE_CHECK_CONNECT = 'snowflake.can_connect'
+    SERVICE_CHECK_CONNECT = 'can_connect'
 
     def __init__(self, *args, **kwargs):
         super(SnowflakeCheck, self).__init__(*args, **kwargs)
diff --git a/snowflake/tests/test_snowflake.py b/snowflake/tests/test_snowflake.py
index d89b1dbf4e670..140ffdf46a3bf 100644
--- a/snowflake/tests/test_snowflake.py
+++ b/snowflake/tests/test_snowflake.py
@@ -1,6 +1,7 @@
 # (C) Datadog, Inc. 2020-present
 # All rights reserved
 # Licensed under a 3-clause BSD style license (see LICENSE)
+import copy
 from decimal import Decimal
 from typing import Any, Callable, Dict
 
@@ -13,6 +14,14 @@
 from .common import CHECK_NAME, EXPECTED_TAGS
 
 
+def test_emits_critical_service_check_when_service_is_down(dd_run_check, aggregator, instance):
+    config = copy.deepcopy(instance)
+    config['login_timeout'] = 5
+    check = SnowflakeCheck(CHECK_NAME, {}, [config])
+    dd_run_check(check)
+    aggregator.assert_service_check('snowflake.can_connect', SnowflakeCheck.CRITICAL)
+
+
 def test_storage_metrics(dd_run_check, aggregator, instance):
     # type: (Callable[[SnowflakeCheck], None], AggregatorStub, Dict[str, Any]) -> None