If your investigation gives you reasonable grounds to search a suspect's home, you can apply. There are two kinds of application — read both before you write yours, since they work differently.
Where a suspect has already been arrested for a serious offence, police don't need a magistrate's permission to search premises that person occupies or controls — a senior officer can authorise it directly. This kind of application doesn't count against your search budget.
Where a suspect hasn't been arrested, police need a magistrate's warrant. To get one, you need to show:
Vague suspicion isn't enough — you need to point to something specific you've actually found.