DALLAS — Dallas is facing a revenue gap in fiscal 2012 of at least $41 million, city manager Mary Suhm said Wednesday at the City Council’s first briefing on next year’s budget.

In the worst-case scenario presented to the council, Suhm said, Dallas revenue would fall by $44.7 million and expenditures would be $51.3 million more than in fiscal 2011, producing a $96 million shortfall.

The best-case scenario envisioned a $3 million increase in revenue and only $44 million of additional expenditures.

The figures provided to the council were preliminary, according to Suhm, who noted that they will change before she presents a balanced budget in early August.

She said Texas, which is facing a $27 billion shortfall, may shift some costs to cities as the Legislature balances the two-year state budget. Reduced federal spending could also affect local ­governments, according to Suhm.

The City Council is set to adopt the final budget on Sept. 28. It will go into effect Oct. 1.

Dallas’ $1.9 billion of outstanding GO debt is rated AA-plus by Standard & Poor’s and Aa1 by Moody’s Investors Service.

Most of the difference in the forecast was attributed to uncertainty about property tax revenue.

Suhm said the drop in assessed valuations could be as little as 0.27%, which would result in a revenue decline of $1.7 million. However, if the fall in assessed valuation is 4.23%, the city would realize $27.1 million less than in fiscal 2011.

Assessed valuations fell 3.6% in fiscal 2010 and 4.4% in fiscal 2011 after going up 6.4% annually between 2005 and 2009. Total valuations declined to $83 billion in fiscal 2011 from $90 billion in fiscal 2009.

The total valuation includes $39.6 billion of residential properties, $31.5 billion of commercial properties, and $12.3 billion of business personal properties.

The council raised Dallas’ property-tax rate by almost 5 cents to $7.97 per $1,000 of assessed value in September 2010. The additional $39 million generated by the increase helped ease an estimated $200 million shortfall in fiscal 2011.

Several City Council members said they are reluctant to raise the property tax again.

One bright spot in Suhm’s revenue estimate was an increase in sales tax collections of between $5 million and $1.7 million.

Balancing the fiscal 2011 budget required 46 employee layoffs and pay cuts for all city workers, including police and firefighters. Employees were also given five to eight days of unpaid leave.

Without the higher property tax rate and other adjustments, 442 employees would have been laid off.

The $2.8 billion Dallas budget for fiscal 2011 includes $2 billion for operations and $822 million of capital improvements. General fund expenditures fell $10 million from fiscal 2010.

Suhm’s budget projections assume a GO bond sale in fiscal 2012 that will cost $4.5 million in debt service next year. Proceeds will be used to retire a portion of the $500 million commercial paper program the council adopted in January 2010.

The commercial paper program was established to keep debt-service payments at a minimum until property tax revenue rebounded.

Dallas has $601 million of authorized but unissued debt remaining from $1.35 billion of GO bonds approved by voters in 2006.

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