"same kind of person" is correct and often used in written English.
It generally refers to someone who is similar in some way, either in characteristics, traits, beliefs, etc. For example, "I'm looking for the same kind of person to join my team who is creative and a hard worker."
The way your personality and level will attract the same kind of person of the same level!
The biggest mistake a president can make is to name the same kind of person over and over".
The burglar goes on to ask, "What kind of person names their parrot Moses?" The parrot replies, "The same kind of person that names his Rottweiler Jesus".
"Well, she and I are exactly the same kind of person, so it's probably only like two points off," explained Ms. Davis with a shy smile.
One can't be the same kind of person all the time.' Still on the subject of other writers, Naipaul questions me eagerly, and quite closely, about Philip Roth and Salman Rushdie, affecting to know little of their recent work.
Blakeley said Contreras was the same kind of person last season, but when he went 3-0 with a 1.51 earned run average in September, nobody questioned his mental makeup.
And they want the person to not be the same kind of boring person that they are".
But then we broke up, and I found myself wondering if I was the same kind of white person I'd been before.
After years of living a secret life, she emerges as "the kind of woman common in their family, narrow, censorious, quick to pass judgment," the same kind of disapproving person, in other words, who drove her and her brother from the family home.
I guess the same kind of self-important person who considers it OK to hold a private phone call while being served at the checkout.
Would it be acceptable to make the same kind of joke about a person in a wheelchair or a person of color?
