Audi A4 front parts with emblems are pictured at production line of German car manufacturer's plant in Ingolstadt Thomson Reuters LISBON (Reuters) - Asked by an attendant if she wants a personal invoice on a 15 euro purchase in a Lisbon pet shop, Lucia Miranda excitedly addresses her tiny pooch: "Do we want to win an Audi, au-au? Yes we do. Sure we want the invoice."

It may seem absurd, but the 56-year-old notary is talking sense. A state draw offering fancy cars on invoices issued with individual taxpayer numbers has firmly grabbed the attention of the Portuguese - those hopeful to win and critics alike.

On April 17, the government will give away the first two Audi A4 sedans in what will then be a weekly draw for a year.

"The Lucky Invoice" draw, which will be televised, is aimed at stimulating the fight against tax evasion and the large shadow economy in cash-strapped Portugal where the tax burden is at record levels after years of austerity.

The government says the number of such invoices jumped 45 percent in January - the first month the bills qualified for the lottery - from a year earlier to 46 million.

State Tax Secretary Paulo Nuncio told Reuters that the steep rise "shows the growing level of consumer adherence to the fight against the parallel economy." He estimated that new measures against tax evasion could add between 600 million and 800 million euros in tax revenues in the medium term.

A study by AT Kearney consultants at the end of last year showed that the shadow economy accounted for about one-fifth of Portugal's gross national product, or over 31 billion euros. At 19 percent of GDP, that was almost 7 points above western Europe's average. The study acknowledged that Portugal was a forerunner in taking measures to address tax evasion and fraud.

Other measures in Portugal include greater use of electronic invoicing, investment in technology and more tax agents, as well as small tax discounts on personal invoices, in force from last year. Electronic invoices rose 25 percent in January from a year earlier to around 365 million.

Shop and cafe attendants contacted by Reuters say they have not seen any sharp increase in personal invoicing, although hopeful clients who want to take part in the draw are not rare.

"They don't come in droves. Those who ask for the invoices usually speak about the draw half in jest, like: 'I wouldn't have enough money to service that car' or 'I'd have to sell it to pay my debts'," said Bebiana Azevedo, 44, who works in a clothes store in Lisbon.

Critics, including the consumer protection association, say the measure transforms citizens into revenue service agents and may also be used to monitor individual spending by Portuguese, while the 2 million euros worth of cars would have been better spent on social projects and not on mid-range luxury cars.

"It's a way to control people and it can give a winner more headaches than joy, especially to elderly. I prefer the normal lottery," said Armenio Coelho, a 60-year-old car mechanic.

The draw has given rise to dark humor. One popular caricature depicts a queue of people in rags waiting their turn at a soup kitchen while a loudspeaker above announces: "Will the owners of Audi A4s and A6s please move their vehicles".

Weekly draws will dish out Audi A4 cars, worth some 35,300 euros, and several special draws will offer the pricier luxury A6 that costs around 48,000 euros. The government picked the local distributor of Audis, SIVA, in a tender over the closest competitor BMW.

Customers requesting a bill with their taxpayer number on it in any business establishment automatically qualify for a draw ticket per each 10 euros worth of purchases.

They can verify on the Internet if sellers submitted their invoices to the tax authorities, and in case of any failure on the seller's behalf can submit the bills themselves.

It is that sort of citizen control of tax payments by businesses that the government wants to stimulate, according to the finance ministry, which also denied suggestions of any monitoring of private spending.

(Reporting By Andrei Khalip; Editing by Toby Chopra)