The second-most populous state has largely avoided the worst of the recession. But the latest monthly survey published by the Federal Reserve Bank of Dallas shows manufacturers in the state are on the verge of getting downright downtrodden.

This month’s Texas Manufacturing Outlook Survey showed activity remained “sluggish,” the Fed said Monday.

The production index rose to 5 from minus-2 in June, the Dallas Fed said, suggesting output rose slightly during the month. But the indexes tracking new orders and new order growth dropped into negative territory, while capacity use posted its first negative reading since late 2009.

What’s more, the general business activity index tumbled for the fourth straight month, to minus-21 from minus-4 in June. Three times as many Texas manufacturing firms saw deteriorating economic conditions during the month as saw improving ones.

The index of conditions six months ahead declined as well, falling to 5 from 14 last month. A quarter of businesses expect to see a stronger economy in January 2011, compared with 19% that expect to see a weaker one.

The finding comes at a time when investors are fretting over a likely second-half economic slowdown that some fear could lead to problems in a still fragile banking system. The survey hardly cinches the case for another downturn and all the attendant fears, but it certainly doesn’t make taking an upbeat view any easier either.