Are there any jurisdictions where theft is not a crime, but the owner of a stolen item can sue the thief for either return of the item or monetary damages? This would be similar to how copyright law would work if criminal copyright infringement statutes were repealed.
Theft is universally a crime in virtually every jurisdiction. Insofar as a state has a criminal code and a functioning judiciary, theft will always be a crime. It is also a basic legal principle that theft is a tort as well (in other words, a civil wrong incurring damages to an individual that can be remedied in a court of law).
A key part of the problem in failing to make theft a crime, is that in the absence of a substantive penalty in terms of a fine or imprisonment, theft becomes a low-risk, high-reward activity where the maximum penalty is simply the repayment of stolen goods (with relatively minimal loss). This fails to provide an effective deterrent to this socially frowned-upon activity, and rates of crime would skyrocket. It is appropriate, therefore, to make theft a crime (and all jurisdictions do so), as all pillars of criminal justice immediately apply.
Edit: As @/JBentley correctly points out, penalties do in fact exist in civil law. That said, the power of incarceration, perhaps in this case the ultimate deterrent, is largely unavailable in civil cases. The ultimate point - that theft is rendered a more sound and legitimate enterprise based largely on gambling - remains the same. Additionally, not all individuals have the time or effort to file small claims and follow cases to the end. Making theft a tort-only offense would cause extraordinary difficulties in enforcement as many would consider the loss of perhaps a small article relatively insignificant compared to filing in small claims court.