Write a Python function `check_type(test_tuple)` that checks if all elements in a given tuple have the same data type. The function should return `True` if all elements share the same type, and `False` otherwise.
#### Example Usage
```python [main.nopy]
print(check_type((5, 6, 7, 3, 5, 6))) # Output: True
print(check_type((1, 2, "4"))) # Output: False
print(check_type((3, 2, 1, 4, 5))) # Output: True
```
#### Constraints
- The input will always be a tuple.
- The tuple can contain any type of elements, including mixed types.