The company accused the Rail Maritime and Transport union of failing to comply with the Trade Union and Labour Relations Act of 1992 in the ballot, which showed a 54% majority in favour of strikes.
The case was set to be heard today but Network Rail (NR) said it would now go ahead at the High Court in London at 10am tomorrow.
The union, which has called four days of action from next Tuesday, the day after the Easter break, said it will strongly defend the legal action.
NR said the alleged inaccuracies and discrepancies impacted on almost 300 votes or potential votes.
Robin Gisby, NR's director of operations and customer services, said: "We believe we have uncovered scores of inaccuracies and discrepancies in the RMT's signallers ballot that, in our view, makes it invalid.
"We want to find a negotiated settlement to this dispute and talks continue but we have a responsibility to the entire country to head off this strike and let people enjoy their Easter break."
NR said the inaccuracies included 11 signal boxes balloted by the RMT that do not exist, with most having been closed for years; 67 locations where the numbers of RMT members balloted exceeded the total number of employees working there; 26 workplaces which were completely missed out, giving RMT members at these locations no opportunity to vote; and 12 locations where there were no operations staff at all, so workers were ineligible to vote.
The company said one of the signal boxes included in the RMT ballot had been burnt down by arsonists a year ago, and added that it had three employees at South Tottenham, where 11 members had been asked to vote, and 24 employees at Crewe, where the RMT invited 33 members to vote.
The company said it is considering its position in relation to a strike by maintenance workers, but added that if it does go ahead it will have almost no affect on services.
Bob Crow, general secretary of the RMT, said: "RMT is putting together an experienced legal team, including some of the most high-profile employment law experts in the country, and we will be mounting the most robust defence possible in the High Court against this attack by Network Rail on our internal democracy.
"This is a scandalous attempt by Network Rail to use the full weight of the anti-union laws to deny our members their basic human right to withdraw their labour and we will fight this assault on our union to the hilt."
Anthony Smith, chief executive of rail customer watchdog Passenger Focus, said: "Passengers are being left in a state of limbo as unions and Network Rail fight it out in court, in the media and at the negotiating table.
"If this strike goes ahead, three-and-a-half million passengers each day are going to be inconvenienced and annoyed. That cannot be in anyone's long-term interest."
Meanwhile, train firms today published outline revised timetables showing which services will run from April 6-9 if the action is not averted.
The earliest services will begin is 7am and the latest they will end is 7pm.
Northern Rail expects to run a reduced service on certain routes from Bradford, Leeds, Huddersfield, Sheffield, Newcastle and Manchester;
Wharfedale Line: Leeds/Bradford Forster Square – Ilkley (4 trains per hour in each direction)
Airedale Line: Leeds/Bradford Forster Square – Skipton (4 trains per hour in each direction)
Leeds – York (1 train per hour in each direction)
Leeds – Doncaster (2 trains per hour in each direction)
Leeds – Huddersfield / Marsden (1 train per hour in each direction)
Sheffield - Doncaster via Rotherham (2 trains per hour in each direction)
Sheffield – Nottingham (1 Northern service per hour in each direction. East Midland Trains will also operate on this route)
East Coast expects to run near normal services from London King's Cross to Leeds, York, Newcastle, Edinburgh and Glasgow.
CrossCountry expects to run an hourly service between Bristol and Edinburgh via Doncaster, Birmingham and Manchester, Cambridge and Stansted Airport, and Birmingham and Leicester;
First Transpennine Express expects to run a reduced service on certain routes;
Grand Central expects to run two trains daily in each direction with a revised calling pattern;
East Midlands Trains will run a normal daytime service on all routes to London St Pancras from Sheffield, Derby, Nottingham and Leicester. Reduced services will run locally;
Arriva Trains Wales expects to run a reduced service on certain routes to and from Cardiff Central and Cardiff Queen Street, but none on others;
c2c expects to run a reduced main line service between Shoeburyness and London Fenchurch Street via Basildon;
Chiltern Railways will run a reduced service between Bicester, High Wycombe and London Marylebone and between Aylesbury and London Marylebone. Between two and four trains per hour will run from 8am to 6pm;
First Capital Connect expects to run a reduced service on the Great Northern and Thameslink routes, with a bus service between King's Lynn and Ely. There will be no Wimbledon Loop or joint Southeastern services;
First Great Western expects to run mostly hourly services from to and from London Paddington, and a number of other routes;
London Overground will run a reduced service on the London Euston and Watford Junction line;
London Midland expects to run a reduced service of between one and four trains an hour on some routes, but no trains at all on some lines;
Merseyrail expects to run two trains per hour on most lines, but none at all on a small number of routes;
National Express East Anglia and Stansted Express will run a reduced service of two or four trains an hour between London Liverpool Street and certain destinations;
Southern will run a reduced service on certain routes only, and will offer a bus and limited train service between Gatwick and Victoria after 7pm;
Southeastern expects to run a reduced service to and from London Charing Cross, to and from London Victoria, and on the high- speed line to and from London St Pancras;
South West Trains expects to run a reduced service on routes to and from London Waterloo. Buses will also run on parts of the route;
Virgin Trains expects to run a normal service Euston to Glasgow, reduced services Euston to Manchester and to Birmingham, and buses Crewe to Liverpool and to Chester;
Eurostar expects to run a normal service to and from London St Pancras.
Details for services run by remaining train operators are still being finalised.
Information is available on www.nationalrail.co.uk/dispute.