Firstly, you don't seem to be using the DBI in that code, so your title looks inaccurate. Of course, you might be using DBI calls in the "mysql_connect" function, but we don't know.

But to answer your question, the answer is that it depends on the rest of your code. What happens to the $dbh object? Does it go out of scope at the end of the function? Or is it returned from the function and stored in a different variable? Without seeing more of the structure of your code it's impossible to give any firm answers.