Make sure you have a good reason for the check. It will only be accepted to counter vandalism or disruption to Wikimedia wikis. Valid reasons include needing a block of the underlying IP or IP range, disruptive sockpuppetry, vote-stacking, and similar disruption where the technical evidence from running a check would prevent or reduce further disruption.
Be specific in your reasons. Ambiguous or insufficient reasons will cause delays. Explain the disruption and why you believe the accounts are related, ideally using diff links or other evidence.
Make sure there are no local checkusers or policies.
Reason(s): Two users on Persian Wikipedia believe that the above mentioned accounts belong to the same person. They mostly edit articles related to the conflict between Israel and Hamas and both are against Israel policies. Also their edit intersection (10 articles) is rather high relative to their total number of edits (Kharmagass has 328 edits and سپاهی has 68 edits). This may be a case of inappropriate usage of alternative accounts by contributing to the same page. Dalba 16:49, 22 August 2014 (UTC)
Are they abusing their use? Are they double voting? Are they co-participating in editing conflicts? At this point of time, a suspicion in a controversial area, where there will be a swathe of editors to manage issues, does not seem sufficient to run a checkuser. There needs to a specific issue that is going to be resolved. — billinghurstsDrewth 23:18, 22 August 2014 (UTC)
Editing with two different accounts on the same page, by itself, is an abuse according to en:WP:ILLEGIT. There is indeed an edit war -- to be fair, some may call it a slight one -- going on in the articles between users. For example here Kharmagass and سپاهی are trying to change the phrase "the old land of Israel" to "the old land of Palestine" but other users have reverted their edits. (I know that the abuse is not so obvious as trying to circumvent the three-revert rule, but again if it was then the admins probably could have blocked them based on the duck test and there was no need to checkuser anymore). Dalba 03:26, 23 August 2014 (UTC)
@دالبا:I think that you are applying a stringent test on a policy. It is my opinion that unless there is a significant level of misuse, a checkuser for that level of discourse is overkill. That said, if you insist, then I will undertake it, though the only result at best will be you get to a block an account. — billinghurstsDrewth 04:05, 23 August 2014 (UTC)