The Bible forbids a believer to take his brother in Christ to court (see 1 Corinthians 6) but there is no specific prohibition in the Word that I know of which would forbid initiating litigation against an unbeliever.
That being said, we are never free from our obligation to reflect the love of Christ, especially to unbelievers. Nor are we at liberty to violate the command to love our enemies. (Matthew 5:44) For these reasons, I think it's critical for any believer in Christ to prayerfully search their heart before engaging in any kind of legal action. If there is even the slightest hint of any attitude or consideration that is unchristlike, such as greed, unforgiveness, revenge or bitterness, I would strongly advise against moving forward with legal action of any kind. In such a case, it would be better to be wronged or cheated than to engage in court proceedings with improper motives.