Simply put, you can work with the file in a block Try/Catch, in the event of exceptions, for example IOException, Voce checks the error code returned, if it is ERROR_SHARING_VIOLATION or ERROR_LOCK_VIOLATION, the file is in use.
In accordance with this answer, you can implement it as follows:
public bool ArquivoEmUso (string arquivo) {
    try {
        using (File.Open(arquivo, FileMode.Open)) {}
    }
    catch (IOException e) {
        var errorCode = Marshal.GetHRForException(e) & ((1 << 16) - 1);
        return errorCode == 32 || errorCode == 33;
    }
    return false;
}
Another, more appropriate way is to use the API Restart Manager, According to the page How do I find out which process has an open file?, in English, the purpose of this API is:
The official objective of Restart Manager is to help make it possible
  shut down and restart the applications that are using a file that
  you wish to update.
In order to do this, it needs to keep track of which processes
  are holding references to which files. [...]
This answer of SOEN suggests to implement this as follows: 
static public class FileUtil {
    [StructLayout(LayoutKind.Sequential)]
    struct RM_UNIQUE_PROCESS {
        public int dwProcessId;
        public System.Runtime.InteropServices.ComTypes.FILETIME ProcessStartTime;
    }
    const int RmRebootReasonNone = 0;
    const int CCH_RM_MAX_APP_NAME = 255;
    const int CCH_RM_MAX_SVC_NAME = 63;
    enum RM_APP_TYPE {
        RmUnknownApp = 0, RmMainWindow = 1, RmOtherWindow = 2, RmService = 3,
        RmExplorer = 4, RmConsole = 5, RmCritical = 1000
    }
    [StructLayout(LayoutKind.Sequential, CharSet = CharSet.Unicode)]
    struct RM_PROCESS_INFO {
        public RM_UNIQUE_PROCESS Process;
        [MarshalAs(UnmanagedType.ByValTStr, SizeConst = CCH_RM_MAX_APP_NAME + 1)]
        public string strAppName;
        [MarshalAs(UnmanagedType.ByValTStr, SizeConst = CCH_RM_MAX_SVC_NAME + 1)]
        public string strServiceShortName;
        public RM_APP_TYPE ApplicationType;
        public uint AppStatus;
        public uint TSSessionId;
        [MarshalAs(UnmanagedType.Bool)]
        public bool bRestartable;
    }
    [DllImport("rstrtmgr.dll", CharSet = CharSet.Unicode)]
    static extern int RmRegisterResources(uint pSessionHandle,
                                          UInt32 nFiles,
                                          string[] rgsFilenames,
                                          UInt32 nApplications,
                                          [In] RM_UNIQUE_PROCESS[] rgApplications,
                                          UInt32 nServices,
                                          string[] rgsServiceNames);
    [DllImport("rstrtmgr.dll", CharSet = CharSet.Auto)]
    static extern int RmStartSession(out uint pSessionHandle, int dwSessionFlags, 
                                     string strSessionKey);
    [DllImport("rstrtmgr.dll")]
    static extern int RmEndSession(uint pSessionHandle);
    [DllImport("rstrtmgr.dll")]
    static extern int RmGetList(uint dwSessionHandle,
                                out uint pnProcInfoNeeded,
                                ref uint pnProcInfo,
                                [In, Out] RM_PROCESS_INFO[] rgAffectedApps,
                                ref uint lpdwRebootReasons);
    /// <summary>
    /// Encontra quais processo(s) têm um bloqueio no arquivo especificado
    /// </summary>
    /// <param name="path">Caminho do arquivo</param>
    /// <returns>Processo(s) que bloqueiam o arquivo</returns>
    /// <remarks>Veja também:
    /// http://msdn.microsoft.com/en-us/library/windows/desktop/aa373661(v=vs.85).aspx
    /// http://wyupdate.googlecode.com/svn-history/r401/trunk/frmFilesInUse.cs
    /// </remarks>
    static public List<Process> WhoIsLocking(string path) {
        uint handle;
        string key = Guid.NewGuid().ToString();
        List<Process> processes = new List<Process>();
        int res = RmStartSession(out handle, 0, key);
        if (res != 0) 
          throw new Exception("Não foi possível iniciar a sessão de reinício. Não foi possível determinar arquivo bloqueador.");
        try {
            const int ERROR_MORE_DATA = 234;
            uint pnProcInfoNeeded = 0,
                 pnProcInfo = 0,
                 lpdwRebootReasons = RmRebootReasonNone;
            // Apenas verificando em um recurso
            string[] resources = new string[] { path };
            res = RmRegisterResources(handle, (uint)resources.Length, resources, 0, null, 0, null);
            if (res != 0) throw new Exception("Não foi possível registrar o recurso.");
            //Nota: Há uma condição de corrida aqui - a primeira chamada de RmGetList() 
            //retorna o número total de processos. No entanto, quando chamamos RmGetList()
            //novamente para obter os processos reais, este número pode ter aumentado.
            res = RmGetList(handle, out pnProcInfoNeeded, ref pnProcInfo, null, ref lpdwRebootReasons);
            if (res == ERROR_MORE_DATA) {
                // Criar um array para armazenar os resultados
                RM_PROCESS_INFO[] processInfo = new RM_PROCESS_INFO[pnProcInfoNeeded];
                pnProcInfo = pnProcInfoNeeded;
                // Obtém a lista 
                res = RmGetList(handle, out pnProcInfoNeeded, ref pnProcInfo, processInfo, ref lpdwRebootReasons);
                if (res == 0) {
                    processes = new List<Process>((int)pnProcInfo);
                    //Enumerar todos os resultados e adiciona na lista a ser devolvida
                    for (int i = 0; i < pnProcInfo; i++) {
                        try {
                            processes.Add(Process.GetProcessById(processInfo[i].Process.dwProcessId));
                        }
                        //Capturar o erro - no caso de o processo não está sendo executado
                        catch (ArgumentException) { }
                    }
                }
                else throw new Exception("Não foi possível listar os processos do recurso bloqueador.");
            }
            else if (res != 0) throw new Exception("Não foi possível listar os processos de recurso bloqueador. Falha ao obter o tamanho do resultado.");
        }
        finally {
            RmEndSession(handle);
        }
        return processes;
    }
}
It is necessary to include namespaces:
using System.Runtime.InteropServices;
using System.Diagnostics;
using System.IO;
Example of use:
static void Main(string[] args) {
    string arquivo = @"C:\Path\Do\Arquivo";
    List<Process> processos = FileUtil.WhoIsLocking(arquivo);
    foreach (Process processo in processos) {
        Console.WriteLine(string.Format("O arquivo {0} está em uso!", Path.GetFileName(arquivo)));
        Console.WriteLine(string.Format("Nome do Processo {0}, PID: {1}", processo.ProcessName, processo.Id));
    }
    Console.ReadLine();
}
Imagery:

Note: To API Restart Manager is available from Windows Server 2008 and Windows Vista.
Article on the subject: Restart Manager and Generic Method Compilation - MSDN Magazine
							
							
						 
"I know this happens because some other routine of mine must be locking the file" - so there are several threads accessing the same file? Then the solution is to find the race condition and properly synchronize the threads.
– dcastro