"What proof do we need to initiate eviction procedures"
You will need "preponderance of the evidence". So document everything. Check with Police to see if any related charges or incidents your suspected tenant may have. Lack of evidence in evicting means the tenant can sue you for attorney fees, court cost and damages. An attorney may be the course of action you may need to take. If the lease or rental agreement is near ending, you may wish to non-renew it.
Overall, you should have a "Crime/Drug Addendum" that each tenant signs. That will help make it easier to evict.