Both are correct.. but "cuantos perros tu tienes" means something like "as many dogs you have". If you meant "cuantos perros tu tienes?" and "cuantos perros tienes tu?", both are correct.. but the first one is basically weird due to it's unusual word order. In general, avoid the use of "tu" among the other pronouns, these are used to emphasize the subject, and only when It's needed to emphasize it. "cuantos perros tienes?" Will be better.

¿Cuántos perros tienes?

¿cuántos perros tiene tú?

¿Cuántos perros tienes? o ¿Cuántos perros tienes tú? solo que el tú es como un agregado