Can a company make me pay back relocation expenses?

If there was no relocation repayment agreement, then your employer probably can't make you repay the relocation expenses. Even if there is a relocation repayment contract, many employers won't enforce it if there is a good reason why you left early, perhaps they don't want to be seen as a hardline employer, or, more likely, it would be more expensive to sue you for the relocation expenses than the cost of the expenses themselves.

If you are concerned, your best first step is to contact an employment lawyer regarding the law in the state where you work. He or she will look at your contract and advise you more fully regarding your rights.

It is also possible that a company has an informal policy of enforcement. For example, the company might have a 2/3rds rule: you leave after 12 months, they'd forget about it. On the other hand, if you left after 6 months, you'd be billed for 2/3rds. References would be withheld until you anted up.