Refreezing
Once food is thawed in the refrigerator, it is safe to refreeze it without cooking, although there may be a loss of quality due to the moisture lost through thawing. After cooking raw foods which were previously frozen, it is safe to freeze the cooked foods. If previously cooked foods are thawed in the refrigerator, you may refreeze the unused portion. Freeze leftovers within 3-4 days. Do not refreeze any foods left outside the refrigerator longer than 2 hours; 1 hour in temperatures above 90 °F.
If you purchase previously frozen meat, poultry or fish at a retail store, you can refreeze if it has been handled properly.
I won't even buy fish from the grocery store.
If it's labeled as "previously frozen," then no. Do not re-freeze it.
OK, the USDA disagrees with me...
then where do you get fish from?
I won't even buy fish from the grocery store.
Local fish market
Costco sometimes has decent fish too and yes, you can refreeze it.
Can't seem to find a legit grocery store here that sells no previously frozen fish. The only ones are the Asian markets and I question their standards.
I've found asian markets usually have better fish than grocery stores (not specialty meat markets). Well, asian markets that sell whole fish anyway. You can check the freshness for yourself--cloudiness in the eyes, smell, pressure test.
I'm sure it depends on where you live. Every time I have been to an Asian market, it smells like fish, and good fish doesn't smell fishy. The fish in the grocery store usually looks pretty good and is flash frozen at sea so I am fine with that.