diff --git a/.github/CHANGELOG.md b/.github/CHANGELOG.md
index 450625b31..a664c6634 100644
--- a/.github/CHANGELOG.md
+++ b/.github/CHANGELOG.md
@@ -32,6 +32,9 @@
 * Replace the `dummy_tensor_update` method with the `cutensornetStateCaptureMPS`API to ensure that further gates apply is allowed after the `cutensornetStateCompute` call.
   [(#1028)](https://github.com/PennyLaneAI/pennylane-lightning/pull/1028/)
 
+* Add unit test for measurement with shots for Lightning Tensor with `tn` method.
+  [(#1027)](https://github.com/PennyLaneAI/pennylane-lightning/pull/1027)
+
 * Update the python layer UI of Lightning Tensor.
   [(#1022)](https://github.com/PennyLaneAI/pennylane-lightning/pull/1022/)
 
diff --git a/tests/conftest.py b/tests/conftest.py
index 178982bbe..16bf95b13 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -195,12 +195,22 @@ def _device(wires, shots=None):
 # General LightningStateVector fixture, for any number of wires.
 @pytest.fixture(
     scope="function",
-    params=[np.complex64, np.complex128],
+    params=(
+        [np.complex64, np.complex128]
+        if device_name != "lightning.tensor"
+        else [
+            [c_dtype, method]
+            for c_dtype in [np.complex64, np.complex128]
+            for method in ["mps", "tn"]
+        ]
+    ),
 )
 def lightning_sv(request):
     def _statevector(num_wires):
         if device_name == "lightning.tensor":
-            return LightningStateVector(num_wires=num_wires, c_dtype=request.param)
+            return LightningStateVector(
+                num_wires=num_wires, c_dtype=request.param[0], method=request.param[1]
+            )
         return LightningStateVector(num_wires=num_wires, dtype=request.param)
 
     return _statevector
diff --git a/tests/lightning_qubit/test_measurements_class.py b/tests/lightning_qubit/test_measurements_class.py
index 8e73a5b13..ced0c0e1f 100644
--- a/tests/lightning_qubit/test_measurements_class.py
+++ b/tests/lightning_qubit/test_measurements_class.py
@@ -545,7 +545,12 @@ def test_single_return_value(self, shots, measurement, observable, lightning_sv,
 
         # a few tests may fail in single precision, and hence we increase the tolerance
         if shots is None:
-            assert np.allclose(result, expected, max(tol, 1.0e-4))
+            assert np.allclose(
+                result,
+                expected,
+                max(tol, 1.0e-4),
+                1e-6 if statevector.dtype == np.complex64 else 1e-8,
+            )
         else:
             # TODO Set better atol and rtol
             dtol = max(tol, 1.0e-2)
@@ -788,6 +793,9 @@ def test_controlled_qubit_gates(self, operation, n_qubits, control_value, tol, l
                 tape = qml.tape.QuantumScript(ops, measurements)
 
                 statevector = lightning_sv(n_qubits)
+                if device_name == "lightning.tensor" and statevector.method == "tn":
+                    pytest.skip("StatePrep not supported in lightning.tensor with the tn method.")
+
                 statevector = get_final_state(statevector, tape)
                 m = LightningMeasurements(statevector)
                 result = measure_final_state(m, tape)
@@ -845,6 +853,9 @@ def test_cnot_controlled_qubit_unitary(self, control_wires, target_wires, tol, l
         )
 
         statevector = lightning_sv(n_qubits)
+        if device_name == "lightning.tensor" and statevector.method == "tn":
+            pytest.skip("StatePrep not supported in lightning.tensor with the tn method.")
+
         statevector = get_final_state(statevector, tape)
         m = LightningMeasurements(statevector)
         result = measure_final_state(m, tape)
@@ -889,6 +900,9 @@ def test_controlled_globalphase(self, n_qubits, control_value, tol, lightning_sv
                     [qml.state()],
                 )
                 statevector = lightning_sv(n_qubits)
+                if device_name == "lightning.tensor" and statevector.method == "tn":
+                    pytest.skip("StatePrep not supported in lightning.tensor with the tn method.")
+
                 statevector = get_final_state(statevector, tape)
                 m = LightningMeasurements(statevector)
                 result = measure_final_state(m, tape)
@@ -967,6 +981,9 @@ def test_state_vector_2_qubit_subset(tol, op, par, wires, expected, lightning_sv
     )
 
     statevector = lightning_sv(2)
+    if device_name == "lightning.tensor" and statevector.method == "tn":
+        pytest.skip("StatePrep not supported in lightning.tensor with the tn method.")
+
     statevector = get_final_state(statevector, tape)
 
     m = LightningMeasurements(statevector)