Any suggestions ?

Yes. Don't! The need alone to do that in all of your templates should tell you that something is utterly wrong with that approach. You repeat yourself, and you are writing nasty PHP-level code from years ago.

Templates are meant for separating task, i.e. data gathering and data rendering. Templates are for rendering data, so database connections don't belong in a template. See e.g. The Model View Controller pattern in web applications for a good start into Model View Controller (MVC).

update: Template::Plugin::DBI is a clever module which eases doing the wrong thing, imho. I'd never use it.

You can do it the same was way, almost, as the CGI and you should probably modify your CGI call. Something like this–

my %vars = ( cgi => CGI->new(),
             dbh => DBI->connect([connection params]),
           );
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You can just follow the regular docs for those modules then. It's sometimes terribly convenient to code DB calls and such inside templates (hence PHP's rapid rise) but it's usually a bad long term design choice.

Try putting your USE DBI directive in a separate template then use Template's PRE_PROCESS option.