The contractor was paid for work he did not do...can i have him arrested?
And now for a legally ACCURATE answer...
Depending on the FULL FACTS, there are some scenarios that could lead to an arrest warrant.
If you can PROVE that he committed fraud, then the prosecutor MIGHT pursue charges against him.
If you can PROVE that he stole the money from you (theft), then the prosecutor MIGHT pursue charges against him.
However, if it is simply a matter of your OPINION that he didn't complete the work... then it is very likely to be viewed as a civil matter.
If you want, go ahead and call the police and tell them your version. They will then decide if the complaint is sufficient to take to the prosecutor.