BEIJING (Reuters) - China's economy rebounded in the second quarter, with capital expenditures recovering from 5-year lows, a private survey showed on Thursday, as higher government spending helped boost the property and construction sectors.

The quarterly survey of over 3,000 firms by China Beige Book International (CBB) also showed better hiring and a strong rebound in the services sector, which if sustainable would point to progress in Beijing's long-stated goal of rebalancing the economy.

The "Beige Book" findings contrast to some degree with official data and some other private surveys which point to some steadying in certain parts of the economy but weakness elsewhere.

Official data had shown a pick-up in March but readings for April and May suggested that improvement may be short-lived. Private investment growth has shrunk to a record low, putting more of the burden on state-controlled firms to support economic growth.

Economists have questioned China's official statistics for years and increasingly turn to private surveys such as the CBB and measures such as concrete, steel or electricity production to better gauge trends in the world's second-largest economy.

CBB said China's record credit expansion this year is filtering through to the construction sector, where 43 percent of residential builders reported higher revenue growth in the second quarter, up from 33 percent for the same period last year.

CBB also believes private investment will start to recover in coming months. Its data showed 47 percent of private firms reported faster growth in capital expenditures in the second quarter, up from 32 percent in the first quarter.

Hiring accelerated from the first quarter, with 37 percent of firms increasing headcount, up slightly on-year, though most of the hiring was at very small firms.

Despite the improvement, CBB CEO Leland Miller is not optimistic the positive trends in the second quarter will last, and also has concerns about China's willingness to go through a painful rebalancing process.

"If they are able to (stop relying on debt-fueled growth and stimulus), China's economy will slow, but as it does the economy will rebalance and they will use stimulus to cushion the rebalancing," Miller told Reuters in an interview.

"You'll have a slower growing, healthier China emerge out of the other side."

Policymakers should take the stronger second quarter performance as a chance to push through economic reforms, Miller said.

"The problem is until we see China willing to do the hard work on overcapacity and some of the problems in the economy, I don't have much confidence they can maintain these trends (we saw in the second quarter)."

Miller said there have been no signs of a reduction in industrial production capacity or employment stresses in a sector expected to see millions of lost jobs over the next few years.

"None of this tackling of overcapacity that they've been talking about is panning out in the data. If anything, it's going in the other direction in some ways."

CBB added that the fallout from Britain's vote last week to leave the European Union also posed "significant downside risk" to the Chinese economy, though the implications will take time to pan out.

"Brexit itself will have little impact on China, but global responses to Brexit could put pressure on export-sensitive sectors and financial decision-makers, in particular."

Miller said there is no question there was an improvement in the second quarter, but that financial markets should not be looking for a return to faster growth.

"There's no chance that China has bottomed out. The idea that China has bottomed out should be stricken from the lexicon, because China is on a long-term slowdown. The question is whether they can engineer this the way they want or whether the circumstances are dictated to them."

(Reporting by Elias Glenn; Editing by Kim Coghill)