This situation is one of Double Insurance. In such cases, one of the policies is cancelled, provided there are no claims reported in either of the policies.
Refund is granted on a pro rata basis for the period both the policies are in force concurrently. If one policy is applicable during the period 1.1.2000 to 31.12.2000, while the other is from 1.3.2000 to 28.2.2001. In case the first policy is cancelled on 1.4.2000, refund is made on pro rata basis for the period 2.4.2000 to 31.12.2000. In case the second policy is cancelled on 1.4.2000, then the refund is made for the period 2.4.2000 to 28.2.2001.
However if there is a claim on 1.4.2000, clearly both the policies will cover it. In such cases, the Contribution Condition of the policy is invoked, which states that each of the policies will bear its rateable proportion of the claim.